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Golubitsky, Martin A.

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Author ID: golubitsky.martin-a Recent zbMATH articles by "Golubitsky, Martin A."
Published as: Golubitsky, M.; Golubitsky, Martin; Golubitsky, Martin A.; Golubitsky, Marty
Homepage: http://people.mbi.ohio-state.edu/golubitsky.4/
External Links: MGP · Wikidata · ORCID · dblp · GND
Documents Indexed: 166 Publications since 1971, including 18 Books
Biographic References: 1 Publication
all top 5

Co-Authors

5 single-authored
39 Stewart, Ian Nicholas
15 Schaeffer, David G.
9 Dellnitz, Michael
8 Wang, Yunjiao
7 Field, Michael J.
5 Antoneli, Fernando jun.
5 Chossat, Pascal
5 Dias, Ana Paula S.
5 Dionne, Benoit
5 Keyfitz, Barbara Lee
5 Melbourne, Ian
5 Nicol, Matthew
4 Buono, Pietro-Luciano
4 Guillemin, Victor W.
4 Knobloch, Edgar
4 Krupa, Martin
4 Langford, William F.
4 Marsden, Jerrold Eldon
4 Shiau, LieJune
4 Tischler, David C.
3 Diekman, Casey O.
3 Josić, Krešimir
3 Török, Andrei
3 Wang, Yangyang
2 Aguiar, Manuela A. D.
2 Aronson, Donald G.
2 Barany, Ernest
2 Best, Janet A.
2 Bressloff, Paul C.
2 Broer, Henk W.
2 Buzano, Ernesto
2 Chillingworth, David R.
2 Cowan, Jack D.
2 Crawford, John David
2 Da Conceição A. Leite, Maria
2 Duncan, William
2 Gillis, David B.
2 Hohmann, Andreas
2 LeBlanc, Victor G.
2 Nijhout, H. Frederik
2 Nordstrøm Jensen, Carsten
2 Palacios, Antonio
2 Pivato, Marcus
2 Postlethwaite, Claire M.
2 Reed, Michael C.
2 Romano, David Gilman
2 Rothschild, Bruce L.
2 Thomas, Peter J.
2 True, Hans
2 van Gils, Stephan A.
2 Vegter, Gert
1 Allgower, Eugene L.
1 Alves-Pinto, Carla
1 Bloch, Anthony M.
1 Böhmer, Klaus
1 Cendra, Hernán
1 Chadam, John M.
1 Chorin, Alexandre Joel
1 Collins, James J.
1 Comanici, Adela N.
1 Desbrun, Mathieu
1 Elmhirst, Toby
1 Epstein, Irving R.
1 Farr, William W.
1 Field, Mike J.
1 Filipski, Natasha
1 Gandhi, Punit
1 Gomes, M. Gabriela M.
1 Gotay, Mark J.
1 Guckenheimer, John M.
1 Hao, Wenrui
1 Hou, Chuanze
1 Huang, Zhengyuan
1 Ihrig, Edwin C.
1 Iooss, Gérard
1 Isenberg, Jim
1 Kaper, Tasso J.
1 Keeler, Emmett B.
1 Krishnaprasad, P.s.
1 Lam, King-Yeung
1 Lauterbach, Reiner
1 Leite, Maria Conceição A.
1 Li, Kaitai
1 Lim, Chjan C.
1 Lou, Yuan
1 Luss, Dan
1 Ma, Jun
1 Mallet-Paret, John Joseph
1 Mao, Jianmin
1 Marsden, Alison L.
1 McMillen, Tyler
1 Messi, Leopold Matamba
1 Montgomery, Richard
1 Ortiz, Michael
1 Pinto, Carla M. A.
1 Ratiu, Tudor Stefan
1 Raugel, Geneviève
1 Roberts, Richard Mark
1 Rothschild, Michael
1 Scheurle, Jürgen
...and 16 more Co-Authors
all top 5

Serials

13 Physica D
12 Nonlinearity
12 SIAM Journal on Applied Dynamical Systems
6 Journal of Nonlinear Science
5 Journal of Mathematical Biology
5 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
4 SIAM Journal on Mathematical Analysis
3 Archive for Rational Mechanics and Analysis
3 Communications on Pure and Applied Mathematics
3 Journal of Differential Equations
3 SIAM Journal on Applied Mathematics
3 Dynamical Systems
2 Communications in Mathematical Physics
2 Bulletin of Mathematical Biology
2 Advances in Mathematics
2 Proceedings of the American Mathematical Society
2 Dynamics and Stability of Systems
2 Bulletin of the American Mathematical Society. New Series
2 Notices of the American Mathematical Society
2 Discrete and Continuous Dynamical Systems
2 Chaos
2 Applied Mathematical Sciences
2 Graduate Texts in Mathematics
2 The Journal of Mathematical Neuroscience
1 Journal of Mathematical Analysis and Applications
1 Journal of Mathematical Physics
1 Mathematical Biosciences
1 ZAMP. Zeitschrift für angewandte Mathematik und Physik
1 Inventiones Mathematicae
1 Journal of Differential Geometry
1 Pacific Journal of Mathematics
1 Philosophical Transactions of the Royal Society of London. Ser. A
1 Theoretical Population Biology
1 Transactions of the American Mathematical Society
1 Delft Progress Report
1 Neural Computation
1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
1 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
1 SIAM Review
1 Journal of Dynamics and Differential Equations
1 Philosophical Transactions of the Royal Society of London. Series A
1 Tatra Mountains Mathematical Publications
1 Bulletin of the American Mathematical Society
1 Contemporary Mathematics
1 Fields Institute Communications
1 The IMA Volumes in Mathematics and its Applications
1 ISNM. International Series of Numerical Mathematics
1 Progress in Mathematics
1 São Paulo Journal of Mathematical Sciences
1 Dynamic Games and Applications
1 Journal of Theoretical Biology

Publications by Year

Citations contained in zbMATH

146 Publications have been cited 4,013 times in 2,396 Documents Cited by Year
Stable mappings and their singularities. Zbl 0294.58004
Golubitsky, M.; Guillemin, V.
587
1973
Singularities and groups in bifurcation theory. Volume II. Zbl 0691.58003
Golubitsky, Martin; Stewart, Ian; Schaeffer, David G.
559
1988
Singularities and groups in bifurcation theory. Volume I. Zbl 0607.35004
Golubitsky, Martin; Schaeffer, David G.
454
1985
The symmetry perspective. From equilibrium to chaos in phase space and physical space. Zbl 1031.37001
Golubitsky, Martin; Stewart, Ian
116
2002
A theory for imperfect bifurcation via singularity theory. Zbl 0409.58007
Golubitsky, M.; Schaeffer, D.
113
1979
Nonlinear dynamics of networks: the groupoid formalism. Zbl 1119.37036
Golubitsky, Martin; Stewart, Ian
105
2006
Symmetry groupoids and patterns of synchrony in coupled cell networks. Zbl 1089.34032
Stewart, Ian; Golubitsky, Martin; Pivato, Marcus
102
2003
Patterns of synchrony in coupled cell networks with multiple arrows. Zbl 1090.34030
Golubitsky, Martin; Stewart, Ian; Török, Andrei
98
2005
Hopf bifurcation in the presence of symmetry. Zbl 0588.34030
Golubitsky, Martin; Stewart, Ian
96
1985
Bifurctions, patterns and symmetry. Selected papers dedicated to the memory of John David Crawford. Zbl 0956.00057
Golubitsky, M. (ed.); Knobloch, E. (ed.)
73
2000
Classification and unfoldings of degenerate Hopf bifurcations. Zbl 0442.58020
Golubitsky, Martin; Langford, William F.
64
1981
Imperfect bifurcation in the presence of symmetry. Zbl 0467.58019
Golubitsky, M.; Schaeffer, D.
53
1979
Symmetries and pattern selection in Rayleigh-Bénard convection. Zbl 0599.76098
Golubitsky, M.; Swift, J. W.; Knobloch, E.
50
1984
Symmetry-increasing bifurcation of chaotic attractors. Zbl 0668.58038
Chossat, P.; Golubitsky, M.
49
1988
A modular network for legged locomotion. Zbl 1039.92009
Golubitsky, Martin; Stewart, Ian; Buono, Pietro-Luciano; Collins, J. J.
39
1998
Symmetry in chaos. A search for pattern in mathematics, art and nature. Zbl 0765.58001
Field, Michael; Golubitsky, Martin
38
1992
Pattern selection with \(\mathrm{O}(3)\) symmetry. Zbl 0581.22021
Ihrig, E.; Golubitsky, M.
36
1984
Bifurcation on the hexagonal lattice and the planar Bénard problem. Zbl 0622.76052
Buzano, E.; Golubitsky, M.
36
1983
Heteroclinic cycles involving periodic solutions in mode interactions with \(O(2)\) symmetry. Zbl 0737.58042
Melbourne, I.; Chossat, P.; Golubitsky, M.
35
1989
Boundary conditions and mode jumping in the buckling of a rectangular plate. Zbl 0414.73036
Schaeffer, David; Golubitsky, Martin
35
1979
Models of central pattern generators for quadruped locomotion. I: Primary gaits. Zbl 1039.92007
Buono, Pietro-Luciano; Golubitsky, Martin
33
2001
Symmetry and stability in Taylor-Couette flow. Zbl 0603.76053
Golubitsky, Martin; Stewart, Ian
32
1986
Hopf bifurcation with dihedral group symmetry: coupled nonlinear oscillators. Zbl 0602.58038
Golubitsky, Martin; Stewart, Ian
32
1986
Coupled cells with internal symmetry. I: Wreath products. Zbl 0894.58049
Dionne, Benoit; Golubitsky, Martin; Stewart, Ian
31
1996
Convergence of the age structure: applications of the projective metric. Zbl 0297.92014
Golubitsky, Martin; Keeler, Emmett B.; Rothschild, Michael
30
1975
Some curious phenomena in coupled cell networks. Zbl 1136.37359
Golubitsky, M.; Nicol, M.; Stewart, I.
29
2004
Bifurcation problems with hidden symmetries. Zbl 0567.58004
Golubitsky, M.; Marsden, J.; Schaeffer, D.
28
1984
Bifurcations from regular quotient networks: A first insight. Zbl 1155.37315
Aguiar, Manuela A. D.; Dias, Ana Paula S.; Golubitsky, Martin; Da Conceição A. Leite, Maria
27
2009
Bifurcation analysis near a double eigenvalue of a model chemical reaction. Zbl 0522.35010
Schaeffer, David G.; Golubitsky, Martin A.
27
1981
Homogeneous three-cell networks. Zbl 1114.34035
Leite, Maria da Conceição A.; Golubitsky, Martin
26
2006
Coupled arrays of Josephson junctions and bifurcation of maps with \(S_ N\) symmetry. Zbl 0803.58040
Aronson, D. G.; Golubitsky, Martin; Krupa, Martin
26
1991
The structure of symmetric attractors. Zbl 0805.58043
Melbourne, Ian; Dellnitz, Michael; Golubitsky, Martin
24
1993
Ponies on a merry-go-round in large arrays of Josephson junctions. Zbl 0732.58031
Aronson, D. G.; Golubitsky, Martin; Mallet-Paret, John
24
1991
Iterates of maps with symmetry. Zbl 0694.58030
Chossat, Pascal; Golubitsky, Martin
23
1988
Generic bifurcation of Hamiltonian systems with symmetry. With an appendix by Jerrold Marsden. Zbl 0612.58013
Golubitsky, Martin; Stewart, Ian
23
1987
Coupled cells with internal symmetry. II: Direct products. Zbl 0894.58050
Dionne, Benoit; Golubitsky, Martin; Stewart, Ian
22
1996
Planforms in two and three dimensions. Zbl 0774.35055
Dionne, Benoit; Golubitsky, Martin
22
1992
What geometric visual hallucinations tell us about the visual cortex. Zbl 1037.91083
Bressloff, Paul C.; Cowan, Jack D.; Golubitsky, Martin; Thomas, Peter J.; Wiener, Matthew C.
21
2002
Boundary conditions as symmetry constraints. Zbl 0735.35007
Crawford, J. D.; Golubitsky, M.; Gomes, M. G. M.; Knobloch, E.; Stewart, I. N.
20
1991
Bifurcations with O(3) symmetry including applications to the Benard problem. Zbl 0492.58012
Golubitsky, Martin; Schaeffer, David
20
1982
A classification of degenerate Hopf bifurcations with O(2) symmetry. Zbl 0635.34036
Golubitsky, Martin; Roberts, Mark
19
1987
Central pattern generators for bipedal locomotion. Zbl 1100.92011
Pinto, Carla M. A.; Golubitsky, Martin
18
2006
Two-color patterns of synchrony in lattice dynamical systems. Zbl 1066.34049
Wang, Yunjiao; Golubitsky, Martin
18
2005
The constrained Liapunov-Schmidt procedure and periodic orbits. Zbl 0833.58014
Golubitsky, Martin; Marsden, Jerrold E.; Stewart, Ian; Dellnitz, Michael
18
1995
Bifurcations from synchrony in homogeneous networks: linear theory. Zbl 1165.37018
Golubitsky, Martin; Lauterbach, Reiner
17
2009
Time-reversibility and particle sedimentation. Zbl 0717.58049
Golubitsky, Martin; Krupa, Martin; Lim, Chjan
17
1991
Nilpotent Hopf bifurcations in coupled cell systems. Zbl 1141.34324
Elmhirst, Toby; Golubitsky, Martin
16
2006
Heteroclinic cycles in rings of coupled cells. Zbl 1011.34035
Buono, Pietro-Luciano; Golubitsky, Martin; Palacios, Antonio
16
2000
Cycling chaos. Zbl 0886.58077
Dellnitz, Michael; Field, Michael; Golubitsky, Martin; Ma, Jun; Hohmann, Andreas
16
1995
Detecting the symmetry of attractors. Zbl 0783.58042
Barany, Ernest; Dellnitz, Michael; Golubitsky, Martin
16
1993
Contact equivalence for Lagrangian manifolds. Zbl 0295.57018
Golubitsky, M.; Guillemin, V.
16
1975
Scalar and pseudoscalar bifurcations motivated by pattern formation on the visual cortex. Zbl 1017.37025
Bressloff, Paul C.; Cowan, Jack D.; Golubitsky, Martin; Thomas, Peter J.
15
2001
Hopf bifurcation from rotating waves and patterns in physical space. Zbl 0988.76036
Golubitsky, M.; LeBlanc, V. G.; Melbourne, I.
15
2000
Fearful symmetry: is God a geometer? Zbl 0931.00014
Stewart, Ian; Golubitsky, Martin
15
1992
Pattern formation and bistability in flow between counterrotating cylinders. Zbl 0656.76088
Golubitsky, M.; Langford, W. F.
15
1988
Interior symmetry and local bifurcation in coupled cell networks. Zbl 1067.37066
Golubitsky, M.; Pivato, M.; Stewart, I.
14
2004
The geometry of resonance tongues: a singularity theory approach. Zbl 1035.37035
Broer, Henk W.; Golubitsky, Martin; Vegter, Gert
14
2003
Meandering of the spiral tip: an alternative approach. Zbl 0902.58025
Golubitsky, M.; LeBlanc, V. G.; Melbourne, I.
14
1997
Symmetry of attractors and the Karhunen-Loève decomposition. Zbl 0806.76087
Dellnitz, Michael; Golubitsky, Martin; Nicol, Matthew
14
1994
An introduction to catastrophe theory and its applications. Zbl 0389.58007
Golubitsky, Martin
14
1978
Homeostasis, singularities, and networks. Zbl 1369.92040
Golubitsky, Martin; Stewart, Ian
12
2017
Patterns of synchrony in lattice dynamical systems. Zbl 1079.37061
Antoneli, Fernando; Dias, Ana Paula S.; Golubitsky, Martin; Wang, Yunjiao
12
2005
An unfolding theory approach to bursting in fast-slow systems. Zbl 1215.34043
Golubitsky, Martin; Josić, Krešimir; Kaper, Tasso J.
12
2001
Feed-forward networks, center manifolds, and forcing. Zbl 1257.34025
Golubitsky, Martin; Postlethwaite, Claire
11
2012
Target patterns and spirals in planar reaction-diffusion systems. Zbl 0965.35084
Golubitsky, M.; Knobloch, E.; Stewart, I.
11
2000
The Morse lemma in infinite dimensions via singularity theory. Zbl 0525.58013
Golubitsky, Martin; Marsden, Jerrold
11
1983
Synchrony-breaking bifurcation at a simple real eigenvalue for regular networks 1:1-dimensional cells. Zbl 1235.37011
Stewart, Ian; Golubitsky, Martin
10
2011
Winding numbers and average frequencies in phase oscillator networks. Zbl 1130.37345
Golubitsky, M.; Josic, K.; Shea-Brown, E.
10
2006
A qualitative study of the steady-state solutions for a continuous flow stirred tank chemical reactor. Zbl 0448.58001
Golubitsky, M.; Keyfitz, B. L.
10
1980
Stable mappings and their singularities. 2nd corr. printing. Zbl 0434.58001
Golubitsky, M.; Guillemin, V.
10
1980
Stable mappings and their singularities. (Ustojchivye otobrazheniya i ikh osobennosti.) Transl. from the English by A. G. Kushnirenko. Ed. by V. I. Arnol’d. Zbl 0429.58004
Golubitsky, M.; Guillemin, V.
10
1977
Primitive actions and maximal subgroups of Lie groups. Zbl 0265.22024
Golubitsky, Martin
10
1972
Network periodic solutions: full oscillation and rigid synchrony. Zbl 1216.34029
Golubitsky, Martin; Romano, David; Wang, Yunjiao
9
2010
Stability computations for nilpotent Hopf bifurcations in coupled cell systems. Zbl 1141.37343
Golubitsky, M.; Krupa, M.
9
2007
Spatiotemporal symmetries in the disynaptic canal-neck projection. Zbl 1129.92015
Golubitsky, Martin; Shiau, Liejune; Stewart, Ian
8
2007
An example of symmetry breaking to heteroclinic cycles. Zbl 0991.34043
Hou, Chuanze; Golubitsky, Martin
8
1997
Symmetric patterns in linear arrays of coupled cells. Zbl 1055.80505
Epstein, Irving R.; Golubitsky, Martin
8
1993
Bifurcations on hemispheres. Zbl 0791.35044
Field, M.; Golubitsky, M.; Stewart, I.
8
1991
Hopf-Hopf mode interactions with O(2) symmetry. Zbl 0656.34020
Chossat, Pascal; Golubitsky, Martin; Keyfitz, Barbara Lee
8
1986
Multiparameter bifurcation theory. Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference held July 14-20, 1985, with support from the National Science Foundation (at Humboldt State University, Arcata, California). Zbl 0587.00009
Golubitsky, Martin (ed.); Guckenheimer, John M. (ed.)
8
1986
A singularity theory analysis of a thermal-chainbranching model for the explosion peninsula. Zbl 0497.58006
Golubitsky, Martin; Keyfitz, Barbara Lee; Schaeffer, David G.
8
1981
Analysis of homeostatic mechanisms in biochemical networks. Zbl 1382.92131
Reed, Michael; Best, Janet; Golubitsky, Martin; Stewart, Ian; Nijhout, H. Frederik
7
2017
Derived patterns in binocular rivalry networks. Zbl 1291.92032
Diekman, Casey O.; Golubitsky, Martin; Wang, Yunjiao
7
2013
Bifurcation on the visual cortex with weakly anisotropic lateral coupling. Zbl 1088.37508
Golubitsky, Martin; Shiau, Lie June; Török, Andrei
7
2003
Patterns in square arrays of coupled cells. Zbl 0889.34033
Gillis, David; Golubitsky, Martin
7
1997
Modulated rotating waves in O(2) mode interactions. Zbl 0681.58029
Crawford, John David; Golubitsky, Martin; Langford, William F.
7
1988
A discussion of symmetry and symmetry breaking. Zbl 0535.58010
Golubitsky, Martin; Schaeffer, David
7
1983
Reduction and dynamics of a generalized rivalry network with two learned patterns. Zbl 1263.37068
Diekman, Casey; Golubitsky, Martin; McMillen, Tyler; Wang, Yunjiao
6
2012
Network periodic solutions: patterns of phase-shift synchrony. Zbl 1245.34043
Golubitsky, Martin; Romano, David; Wang, Yunjiao
6
2012
Symmetry in chaos: a search for pattern in mathematics, art and nature. 2nd ed. Zbl 1173.37001
Field, Michael; Golubitsky, Martin
6
2009
Patterns of oscillation in coupled cell systems. Zbl 1017.37045
Golubitsky, Martin; Stewart, Ian
6
2002
Symmetry detectives for SBR attractors. Zbl 0838.34055
Golubitsky, Martin; Nicol, Matthew
6
1995
Coupled cells: Wreath products and direct products. Zbl 0810.34028
Golubitsky, Martin; Stewart, Ian; Dionne, Benoit
6
1994
Mechanisms of symmetry creation. Zbl 0803.35011
Dellnitz, Michael; Golubitsky, Martin; Melbourne, Ian
6
1992
Primitive subalgebras of exceptional Lie algebras. Zbl 0209.06602
Golubitsky, M.; Rothschild, B.
6
1971
Homeostasis in a feed forward loop gene regulatory motif. Zbl 1397.92179
Antoneli, Fernando; Golubitsky, Martin; Stewart, Ian
5
2018
Network symmetry and binocular rivalry experiments. Zbl 1321.92044
Diekman, Casey O.; Golubitsky, Martin
5
2014
Synchrony versus symmetry in coupled cells. Zbl 1112.34020
Golubitsky, Martin; Stewart, Ian
5
2005
Symmetry and pattern formation in coupled cell networks. Zbl 0987.37041
Golubitsky, Martin; Stewart, Ian
5
1999
Spirals in scalar reaction-diffusion equations. Zbl 0886.58102
Dellnitz, Michael; Golubitsky, Martin; Hohmann, Andreas; Stewart, Ian
5
1995
Infinitesimal homeostasis in three-node input-output networks. Zbl 1436.92009
Golubitsky, Martin; Wang, Yangyang
2
2020
Homeostasis in a feed forward loop gene regulatory motif. Zbl 1397.92179
Antoneli, Fernando; Golubitsky, Martin; Stewart, Ian
5
2018
Homeostasis with multiple inputs. Zbl 1395.92067
Golubitsky, Martin; Stewart, Ian
4
2018
Homeostasis despite instability. Zbl 1392.92024
Duncan, W.; Best, J.; Golubitsky, M.; Nijhout, H. F.; Reed, M.
2
2018
Homeostasis, singularities, and networks. Zbl 1369.92040
Golubitsky, Martin; Stewart, Ian
12
2017
Analysis of homeostatic mechanisms in biochemical networks. Zbl 1382.92131
Reed, Michael; Best, Janet; Golubitsky, Martin; Stewart, Ian; Nijhout, H. Frederik
7
2017
Coordinate changes for network dynamics. Zbl 1362.37051
Golubitsky, Martin; Stewart, Ian
4
2017
Rigid patterns of synchrony for equilibria and periodic cycles in network dynamics. Zbl 1382.92023
Golubitsky, Martin; Stewart, Ian
4
2016
Singularity theory of fitness functions under dimorphism equivalence. Zbl 1352.58008
Wang, Xiaohui; Golubitsky, Martin
3
2016
Symmetry types and phase-shift synchrony in networks. Zbl 1364.34045
Golubitsky, Martin; Messi, Leopold Matamba; Spardy, Lucy E.
2
2016
Normal forms and unfoldings of singular strategy functions. Zbl 1348.91047
Vutha, Amit; Golubitsky, Martin
4
2015
Bifurcations in forced response curves. Zbl 1331.34069
Wiser, Justin; Golubitsky, Martin
1
2015
Symmetry methods in mathematical biology. Zbl 1346.92011
Golubitsky, Martin; Stewart, Ian
1
2015
Network symmetry and binocular rivalry experiments. Zbl 1321.92044
Diekman, Casey O.; Golubitsky, Martin
5
2014
Derived patterns in binocular rivalry networks. Zbl 1291.92032
Diekman, Casey O.; Golubitsky, Martin; Wang, Yunjiao
7
2013
Feed-forward networks, center manifolds, and forcing. Zbl 1257.34025
Golubitsky, Martin; Postlethwaite, Claire
11
2012
Reduction and dynamics of a generalized rivalry network with two learned patterns. Zbl 1263.37068
Diekman, Casey; Golubitsky, Martin; McMillen, Tyler; Wang, Yunjiao
6
2012
Network periodic solutions: patterns of phase-shift synchrony. Zbl 1245.34043
Golubitsky, Martin; Romano, David; Wang, Yunjiao
6
2012
Synchrony-breaking bifurcation at a simple real eigenvalue for regular networks 1:1-dimensional cells. Zbl 1235.37011
Stewart, Ian; Golubitsky, Martin
10
2011
Periodically forced Hopf bifurcation. Zbl 1247.34059
Zhang, Yanyan; Golubitsky, Martin
4
2011
Network periodic solutions: full oscillation and rigid synchrony. Zbl 1216.34029
Golubitsky, Martin; Romano, David; Wang, Yunjiao
9
2010
The abelian Hopf \(H\) mod \(K\) theorem. Zbl 1198.37088
Filipski, Natasha; Golubitsky, Martin
4
2010
Bifurcations from regular quotient networks: A first insight. Zbl 1155.37315
Aguiar, Manuela A. D.; Dias, Ana Paula S.; Golubitsky, Martin; Da Conceição A. Leite, Maria
27
2009
Bifurcations from synchrony in homogeneous networks: linear theory. Zbl 1165.37018
Golubitsky, Martin; Lauterbach, Reiner
17
2009
Symmetry in chaos: a search for pattern in mathematics, art and nature. 2nd ed. Zbl 1173.37001
Field, Michael; Golubitsky, Martin
6
2009
Patterns on growing square domains via mode interactions. Zbl 1151.65069
Comanici, Adela; Golubitsky, Martin
3
2008
Stability computations for nilpotent Hopf bifurcations in coupled cell systems. Zbl 1141.37343
Golubitsky, M.; Krupa, M.
9
2007
Spatiotemporal symmetries in the disynaptic canal-neck projection. Zbl 1129.92015
Golubitsky, Martin; Shiau, Liejune; Stewart, Ian
8
2007
Homogeneous coupled cell networks with \(S_3\)-symmetric quotient. Zbl 1163.34305
Aguiar, M. A. D.; Dias, A. P. S.; Golubitsky, M.; Leite, M. C. A.
4
2007
Geometry of resonance tongues. Zbl 1120.37034
Broer, Henk W.; Golubitsky, Martin; Vegter, Gert
4
2007
Synchrony in lattice differential equations. Zbl 1179.37106
Antonelli, Fernando; Dias, Ana Paula S.; Golubitsky, Martin; Wang, Yunjiao
2
2007
Nonlinear dynamics of networks: the groupoid formalism. Zbl 1119.37036
Golubitsky, Martin; Stewart, Ian
105
2006
Homogeneous three-cell networks. Zbl 1114.34035
Leite, Maria da Conceição A.; Golubitsky, Martin
26
2006
Central pattern generators for bipedal locomotion. Zbl 1100.92011
Pinto, Carla M. A.; Golubitsky, Martin
18
2006
Nilpotent Hopf bifurcations in coupled cell systems. Zbl 1141.34324
Elmhirst, Toby; Golubitsky, Martin
16
2006
Winding numbers and average frequencies in phase oscillator networks. Zbl 1130.37345
Golubitsky, M.; Josic, K.; Shea-Brown, E.
10
2006
Patterns of synchrony in coupled cell networks with multiple arrows. Zbl 1090.34030
Golubitsky, Martin; Stewart, Ian; Török, Andrei
98
2005
Two-color patterns of synchrony in lattice dynamical systems. Zbl 1066.34049
Wang, Yunjiao; Golubitsky, Martin
18
2005
Patterns of synchrony in lattice dynamical systems. Zbl 1079.37061
Antoneli, Fernando; Dias, Ana Paula S.; Golubitsky, Martin; Wang, Yunjiao
12
2005
Synchrony versus symmetry in coupled cells. Zbl 1112.34020
Golubitsky, Martin; Stewart, Ian
5
2005
Bursting in coupled cell systmes. Zbl 1404.92052
Golubitsky, Martin; Josić, Krešimir; Shiau, Liejune
1
2005
Bipedal locomotion. Zbl 1099.92005
Golubitsky, Martin; Alves-Pinto, Carla
1
2005
Some curious phenomena in coupled cell networks. Zbl 1136.37359
Golubitsky, M.; Nicol, M.; Stewart, I.
29
2004
Interior symmetry and local bifurcation in coupled cell networks. Zbl 1067.37066
Golubitsky, M.; Pivato, M.; Stewart, I.
14
2004
Symmetry and pattern formation on the visual cortex. Zbl 1079.92011
Golubitsky, Martin; Shiau, LieJune; Török, Andrei
2
2004
Symmetry groupoids and patterns of synchrony in coupled cell networks. Zbl 1089.34032
Stewart, Ian; Golubitsky, Martin; Pivato, Marcus
102
2003
The geometry of resonance tongues: a singularity theory approach. Zbl 1035.37035
Broer, Henk W.; Golubitsky, Martin; Vegter, Gert
14
2003
Bifurcation on the visual cortex with weakly anisotropic lateral coupling. Zbl 1088.37508
Golubitsky, Martin; Shiau, Lie June; Török, Andrei
7
2003
Bifurcation and planar pattern formation for a liquid crystal. Zbl 1187.82132
Golubitsky, Martin; Chillingworth, David
2
2003
The symmetry perspective. From equilibrium to chaos in phase space and physical space. Zbl 1031.37001
Golubitsky, Martin; Stewart, Ian
116
2002
What geometric visual hallucinations tell us about the visual cortex. Zbl 1037.91083
Bressloff, Paul C.; Cowan, Jack D.; Golubitsky, Martin; Thomas, Peter J.; Wiener, Matthew C.
21
2002
Patterns of oscillation in coupled cell systems. Zbl 1017.37045
Golubitsky, Martin; Stewart, Ian
6
2002
Models of central pattern generators for quadruped locomotion. I: Primary gaits. Zbl 1039.92007
Buono, Pietro-Luciano; Golubitsky, Martin
33
2001
Scalar and pseudoscalar bifurcations motivated by pattern formation on the visual cortex. Zbl 1017.37025
Bressloff, Paul C.; Cowan, Jack D.; Golubitsky, Martin; Thomas, Peter J.
15
2001
An unfolding theory approach to bursting in fast-slow systems. Zbl 1215.34043
Golubitsky, Martin; Josić, Krešimir; Kaper, Tasso J.
12
2001
Bifurctions, patterns and symmetry. Selected papers dedicated to the memory of John David Crawford. Zbl 0956.00057
Golubitsky, M. (ed.); Knobloch, E. (ed.)
73
2000
Heteroclinic cycles in rings of coupled cells. Zbl 1011.34035
Buono, Pietro-Luciano; Golubitsky, Martin; Palacios, Antonio
16
2000
Hopf bifurcation from rotating waves and patterns in physical space. Zbl 0988.76036
Golubitsky, M.; LeBlanc, V. G.; Melbourne, I.
15
2000
Target patterns and spirals in planar reaction-diffusion systems. Zbl 0965.35084
Golubitsky, M.; Knobloch, E.; Stewart, I.
11
2000
Symmetry and pattern formation in coupled cell networks. Zbl 0987.37041
Golubitsky, Martin; Stewart, Ian
5
1999
Symmetry, generic bifurcations, and mode interaction in nonlinear railway dynamics. Zbl 0981.70017
Nordstrøm Jensen, Carsten; Golubitsky, Martin; True, Hans
2
1999
Heteroclinic cycles in systems with \(D_n\) symmetry. Zbl 0981.34030
Buono, Pietro-Luciano; Golubitsky, Martin; Palacios, Antonio
2
1999
Linear algebra and differential equations using MATLAB. Zbl 1329.00009
Golubitsky, Martin; Dellnitz, Michael
1
1999
A modular network for legged locomotion. Zbl 1039.92009
Golubitsky, Martin; Stewart, Ian; Buono, Pietro-Luciano; Collins, J. J.
39
1998
Meandering of the spiral tip: an alternative approach. Zbl 0902.58025
Golubitsky, M.; LeBlanc, V. G.; Melbourne, I.
14
1997
An example of symmetry breaking to heteroclinic cycles. Zbl 0991.34043
Hou, Chuanze; Golubitsky, Martin
8
1997
Patterns in square arrays of coupled cells. Zbl 0889.34033
Gillis, David; Golubitsky, Martin
7
1997
A formula for a symmetry detective. Zbl 0933.37046
Gillis, D.; Golubitsky, M.
1
1997
Coupled cells with internal symmetry. I: Wreath products. Zbl 0894.58049
Dionne, Benoit; Golubitsky, Martin; Stewart, Ian
31
1996
Coupled cells with internal symmetry. II: Direct products. Zbl 0894.58050
Dionne, Benoit; Golubitsky, Martin; Stewart, Ian
22
1996
Symmetries of periodic solutions for planar potential systems. Zbl 0867.34030
Golubitsky, Martin; Mao, Jian-Min; Nicol, Matthew
1
1996
Symmetry in chaos: a search for pattern in mathematics, art and nature. Papeback ed. Zbl 0853.58002
Field, Michael; Golubitsky, Martin
1
1996
The constrained Liapunov-Schmidt procedure and periodic orbits. Zbl 0833.58014
Golubitsky, Martin; Marsden, Jerrold E.; Stewart, Ian; Dellnitz, Michael
18
1995
Cycling chaos. Zbl 0886.58077
Dellnitz, Michael; Field, Michael; Golubitsky, Martin; Ma, Jun; Hohmann, Andreas
16
1995
Symmetry detectives for SBR attractors. Zbl 0838.34055
Golubitsky, Martin; Nicol, Matthew
6
1995
Spirals in scalar reaction-diffusion equations. Zbl 0886.58102
Dellnitz, Michael; Golubitsky, Martin; Hohmann, Andreas; Stewart, Ian
5
1995
Symmetric chaos: how and why. Zbl 1042.37507
Field, Mike; Golubitsky, Martin
3
1995
Time-periodic spatially periodic planforms in Euclidean equivariant partial differential equations. Zbl 0851.35108
Dionne, Benoit; Golubitsky, Martin; Silber, Mary; Stewart, Ian
2
1995
Symmetry of attractors and the Karhunen-Loève decomposition. Zbl 0806.76087
Dellnitz, Michael; Golubitsky, Martin; Nicol, Matthew
14
1994
Coupled cells: Wreath products and direct products. Zbl 0810.34028
Golubitsky, Martin; Stewart, Ian; Dionne, Benoit
6
1994
A note on symmetries of invariant sets with compact group actions. Zbl 0813.58008
Field, Michael; Golubitsky, Martin; Nicol, Matthew
1
1994
The structure of symmetric attractors. Zbl 0805.58043
Melbourne, Ian; Dellnitz, Michael; Golubitsky, Martin
24
1993
Detecting the symmetry of attractors. Zbl 0783.58042
Barany, Ernest; Dellnitz, Michael; Golubitsky, Martin
16
1993
Symmetric patterns in linear arrays of coupled cells. Zbl 1055.80505
Epstein, Irving R.; Golubitsky, Martin
8
1993
An algebraic criterion for symmetric Hopf bifurcation. Zbl 0788.58038
Golubitsky, Martin; Stewart, Ian
3
1993
Fearful Symmetry: Is God a Geometer? Zbl 0784.00011
Stewart, Ian; Golubitsky, Martin
1
1993
Symmetry in chaos. A search for pattern in mathematics, art and nature. Zbl 0765.58001
Field, Michael; Golubitsky, Martin
38
1992
Planforms in two and three dimensions. Zbl 0774.35055
Dionne, Benoit; Golubitsky, Martin
22
1992
Fearful symmetry: is God a geometer? Zbl 0931.00014
Stewart, Ian; Golubitsky, Martin
15
1992
Mechanisms of symmetry creation. Zbl 0803.35011
Dellnitz, Michael; Golubitsky, Martin; Melbourne, Ian
6
1992
Bifurcations with local gauge symmetries in the Ginzburg-Landau equations. Zbl 0758.35073
Barany, Ernest; Golubitsky, Martin; Turski, Jacek
5
1992
Rotating chemical waves in the Gary-Scott model. Zbl 0745.58041
Farr, W. W.; Golubitsky, M.
2
1992
Bifurcation and symmetry. Cross influence between mathematics and applications. Proceedings of a workshop, held Marburg, Germany, June, 2- 14, 1991. Zbl 0745.00023
Allgower, Eugene L. (ed.); Böhmer, Klaus (ed.); Golubitsky, Martin (ed.)
1
1992
Coupled arrays of Josephson junctions and bifurcation of maps with \(S_ N\) symmetry. Zbl 0803.58040
Aronson, D. G.; Golubitsky, Martin; Krupa, Martin
26
1991
Ponies on a merry-go-round in large arrays of Josephson junctions. Zbl 0732.58031
Aronson, D. G.; Golubitsky, Martin; Mallet-Paret, John
24
1991
Boundary conditions as symmetry constraints. Zbl 0735.35007
Crawford, J. D.; Golubitsky, M.; Gomes, M. G. M.; Knobloch, E.; Stewart, I. N.
20
1991
Time-reversibility and particle sedimentation. Zbl 0717.58049
Golubitsky, Martin; Krupa, Martin; Lim, Chjan
17
1991
Bifurcations on hemispheres. Zbl 0791.35044
Field, M.; Golubitsky, M.; Stewart, I.
8
1991
A torus bifurcation theorem with symmetry. Zbl 0695.34041
van Gils, S. A; Golubitsky, M.
2
1990
Heteroclinic cycles involving periodic solutions in mode interactions with \(O(2)\) symmetry. Zbl 0737.58042
Melbourne, I.; Chossat, P.; Golubitsky, M.
35
1989
...and 46 more Documents
all top 5

Cited by 3,023 Authors

64 Stewart, Ian Nicholas
57 Golubitsky, Martin A.
30 Ashwin, Peter
28 Guo, Shangjiang
24 Knobloch, Edgar
20 Chossat, Pascal
20 Melbourne, Ian
19 Dias, Ana Paula S.
18 Lamb, Jeroen S. W.
17 Ikeda, Kiyohiro
17 Marsden, Jerrold Eldon
16 Buono, Pietro-Luciano
16 Krawcewicz, Wieslaw Z.
15 Izumiya, Shyuichi
15 Labouriau, Isabel S.
14 Aguiar, Manuela A. D.
14 Chen, Yushu
14 Dangelmayr, Gerhard
14 Zhang, Chunrui
13 Gaeta, Giuseppe
13 Ha, Seung-Yeal
12 Field, Michael J.
12 Krupa, Martin
12 Saeki, Osamu
12 Schaeffer, David G.
11 Balanov, Zalman I.
11 Broer, Henk W.
11 Healey, Timothy J.
11 Wu, Jianhong
10 Antoneli, Fernando jun.
10 Bridges, Thomas J.
10 Chien, Cheng-Sheng
10 Lauterbach, Reiner
10 Palacios, Antonio
10 Roberts, Richard Mark
10 Romero-Fuster, María Carmen
9 Aston, Philip J.
9 Bressloff, Paul C.
9 Castro, Sofia B. S. D.
9 Chung, Kwok-Wai
9 Dellnitz, Michael
9 Janeczko, Stanisław
9 Laing, Carlo R.
9 Manoel, Miriam
9 Silber, Mary
9 Tchoń, Krzysztof
9 Zheng, Baodong
8 Atanackovic, Teodor M.
8 Greenleaf, Allan
8 Mei, Zhen
8 Pinto, Carla M. A.
7 Furter, Jacques-Elie
7 Holmes, Philip J.
7 Janovský, Vladimír
7 Kevrekidis, Ioannis George
7 Kielhöfer, Hansjörg
7 Kossowski, Marek
7 Langford, William F.
7 Podvigina, Ol’ga Mikhaĭlovna
7 Poláčik, Peter
7 Qin, Wenxin
7 Sanders, Jan A.
7 Wallace, Rodrick
7 Yang, Zhonghua
6 Baptistelli, Patrícia H.
6 Crawford, John David
6 de Jesus, C. Mendes
6 Desroches, Mathieu
6 Gatermann, Karin
6 Kevrekidis, Panayotis G.
6 Keyfitz, Barbara Lee
6 LeBlanc, Victor G.
6 Maier-Paape, Stanislaus
6 Marques, Francisco
6 Medveď, Milan
6 Moehlis, Jeff
6 Moiola, Jorge Luis
6 Murota, Kazuo
6 Reiter, Clifford A.
6 Renardy, Yuriko Yamamuro
6 Rucklidge, Alastair M.
6 Sarti, Alessandro
6 Schecter, Stephen
6 Vianello, Maurizio
6 Wan, Yieh-Hei
6 Wulff, Claudia
5 Armbruster, Dieter
5 Auffray, Nicolas
5 Bick, Christian
5 Böhmer, Klaus
5 Champneys, Alan R.
5 Chan, Bernard S.
5 Chan, H. S. Y.
5 Chen, Guanrong
5 Chillingworth, D. R. J.
5 Cicogna, Giampaolo
5 Citti, Giovanna
5 Cliffe, K. Andrew
5 Damon, James Norman
5 El Naschie, Mohamed Saladin
...and 2,923 more Authors
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Cited in 386 Serials

192 Physica D
108 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
95 Chaos
88 Journal of Differential Equations
52 Chaos, Solitons and Fractals
43 Transactions of the American Mathematical Society
42 Archive for Rational Mechanics and Analysis
40 Journal of Fluid Mechanics
40 Journal of Nonlinear Science
34 Journal of Mathematical Analysis and Applications
34 Nonlinear Dynamics
32 Dynamics and Stability of Systems
32 Nonlinear Analysis. Theory, Methods & Applications
30 Journal of Dynamics and Differential Equations
29 SIAM Journal on Applied Dynamical Systems
28 Mathematical Proceedings of the Cambridge Philosophical Society
27 Journal of Mathematical Biology
24 Journal of Mathematical Economics
23 Journal of Computational and Applied Mathematics
22 Dynamical Systems
21 Bulletin of Mathematical Biology
21 Applied Mathematics and Computation
19 ZAMP. Zeitschrift für angewandte Mathematik und Physik
19 Applied Mathematics and Mechanics. (English Edition)
19 Mathematical and Computer Modelling
19 Physics of Fluids
18 Journal of Mathematical Physics
17 Computer Methods in Applied Mechanics and Engineering
17 Topology and its Applications
16 Communications in Mathematical Physics
16 Journal of Geometry and Physics
16 Linear Algebra and its Applications
15 Advances in Mathematics
15 Journal of Difference Equations and Applications
15 Communications in Nonlinear Science and Numerical Simulation
14 Mathematical Biosciences
14 The Journal of Mathematical Neuroscience
13 Biological Cybernetics
13 Journal of Computational Physics
13 Journal of Economic Theory
13 Proceedings of the American Mathematical Society
13 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
12 Physics Letters. A
12 Journal of Elasticity
12 Journal of Mathematical Sciences (New York)
12 Nonlinear Analysis. Real World Applications
12 Journal of Theoretical Biology
11 Nonlinearity
11 Journal of Soviet Mathematics
11 Mathematische Annalen
11 Systems & Control Letters
11 Bulletin of the American Mathematical Society. New Series
11 Discrete and Continuous Dynamical Systems
10 Acta Mechanica
10 Journal of Statistical Physics
10 Journal of Functional Analysis
10 Journal of Pure and Applied Algebra
9 Computers & Mathematics with Applications
9 Annales de l’Institut Fourier
9 Automatica
9 Functional Analysis and its Applications
9 Inventiones Mathematicae
9 Manuscripta Mathematica
9 Acta Applicandae Mathematicae
9 Annals of Global Analysis and Geometry
9 Journal of Computational Neuroscience
8 International Journal of Engineering Science
8 Journal of the Mechanics and Physics of Solids
8 Computing
8 Duke Mathematical Journal
8 Journal of Optimization Theory and Applications
8 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
8 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
7 Mathematische Zeitschrift
7 Neural Computation
7 SIAM Journal on Mathematical Analysis
7 Annales de l’Institut Henri Poincaré. Physique Théorique
7 Mathematics and Mechanics of Solids
7 Abstract and Applied Analysis
7 Proceedings of the Steklov Institute of Mathematics
6 International Journal of Theoretical Physics
6 Letters in Mathematical Physics
6 Mathematical Methods in the Applied Sciences
6 Cahiers de Topologie et Géométrie Différentielle Catégoriques
6 Geometriae Dedicata
6 Theoretical Population Biology
6 Applied Mathematics Letters
6 MCSS. Mathematics of Control, Signals, and Systems
6 Communications in Partial Differential Equations
6 Qualitative Theory of Dynamical Systems
6 Journal of Fixed Point Theory and Applications
6 Journal of Singularities
6 Symmetry
5 Reports on Mathematical Physics
5 Rocky Mountain Journal of Mathematics
5 Annali di Matematica Pura ed Applicata. Serie Quarta
5 Mathematics and Computers in Simulation
5 Journal of Economic Dynamics & Control
5 Neural Networks
5 European Journal of Applied Mathematics
...and 286 more Serials
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Cited in 61 Fields

756 Dynamical systems and ergodic theory (37-XX)
625 Ordinary differential equations (34-XX)
390 Partial differential equations (35-XX)
355 Biology and other natural sciences (92-XX)
332 Global analysis, analysis on manifolds (58-XX)
231 Fluid mechanics (76-XX)
163 Mechanics of deformable solids (74-XX)
134 Manifolds and cell complexes (57-XX)
132 Numerical analysis (65-XX)
131 Differential geometry (53-XX)
119 Systems theory; control (93-XX)
115 Mechanics of particles and systems (70-XX)
88 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
76 Operator theory (47-XX)
64 Computer science (68-XX)
59 Statistical mechanics, structure of matter (82-XX)
46 Several complex variables and analytic spaces (32-XX)
41 Operations research, mathematical programming (90-XX)
37 Combinatorics (05-XX)
35 Calculus of variations and optimal control; optimization (49-XX)
33 Algebraic geometry (14-XX)
32 Linear and multilinear algebra; matrix theory (15-XX)
32 Classical thermodynamics, heat transfer (80-XX)
32 Quantum theory (81-XX)
31 Group theory and generalizations (20-XX)
30 Information and communication theory, circuits (94-XX)
26 Topological groups, Lie groups (22-XX)
26 Difference and functional equations (39-XX)
23 Probability theory and stochastic processes (60-XX)
21 Optics, electromagnetic theory (78-XX)
20 Algebraic topology (55-XX)
17 Convex and discrete geometry (52-XX)
17 General topology (54-XX)
16 Commutative algebra (13-XX)
15 Integral equations (45-XX)
13 Measure and integration (28-XX)
13 Relativity and gravitational theory (83-XX)
12 General and overarching topics; collections (00-XX)
11 Real functions (26-XX)
10 Statistics (62-XX)
9 History and biography (01-XX)
9 Nonassociative rings and algebras (17-XX)
9 Functional analysis (46-XX)
8 Category theory; homological algebra (18-XX)
7 Functions of a complex variable (30-XX)
7 Geophysics (86-XX)
6 Order, lattices, ordered algebraic structures (06-XX)
6 Geometry (51-XX)
5 Harmonic analysis on Euclidean spaces (42-XX)
5 Integral transforms, operational calculus (44-XX)
5 Astronomy and astrophysics (85-XX)
3 Mathematical logic and foundations (03-XX)
3 Number theory (11-XX)
3 Approximations and expansions (41-XX)
2 Potential theory (31-XX)
2 Abstract harmonic analysis (43-XX)
1 General algebraic systems (08-XX)
1 Field theory and polynomials (12-XX)
1 Special functions (33-XX)
1 Sequences, series, summability (40-XX)
1 Mathematics education (97-XX)

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