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## Shafer, Douglas S.

Compute Distance To:
 Author ID: shafer.douglas-s Published as: Shafer, D. S.; Shafer, Douglas; Shafer, Douglas S.
 Documents Indexed: 41 Publications since 1980, including 1 Book Reviewing Activity: 149 Reviews
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#### Co-Authors

 8 single-authored 11 Romanovski, Valery G. 6 García, Isaac A. 5 Zegeling, André 3 Mahdi, Adam 3 Maza, Susanna 2 Chicone, Carmen C. 2 Jarque, Xavier 2 Levandovskyy, Viktor 2 Llibre, Jaume 2 Rothe, Franz 2 Swanson, Richard C. 2 Walker, Russell Bruce 1 Chen, Xingwu 1 Dumortier, Freddy 1 Edneral, Victor F. 1 Ferčec, Brigita 1 Giné, Jaume 1 Hill, David C. 1 Hu, Zhaoping 1 Pessoa, Claudio 1 Wu, Xiaonan
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#### Serials

 8 Journal of Differential Equations 3 Journal of Dynamics and Differential Equations 2 Journal of the London Mathematical Society. Second Series 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Transactions of the American Mathematical Society 1 Computers & Mathematics with Applications 1 Journal of Mathematical Analysis and Applications 1 Physics Letters. A 1 Rocky Mountain Journal of Mathematics 1 Applied Mathematics and Computation 1 Journal of Geometry 1 Proceedings of the American Mathematical Society 1 Topology 1 Journal of Symbolic Computation 1 Revista Matemática Iberoamericana 1 Applied Mathematics Letters 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Bulletin of the Belgian Mathematical Society - Simon Stevin 1 Discrete and Continuous Dynamical Systems 1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 1 Qualitative Theory of Dynamical Systems 1 Nonlinear Analysis. Real World Applications
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#### Fields

 34 Ordinary differential equations (34-XX) 24 Dynamical systems and ergodic theory (37-XX) 2 Commutative algebra (13-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Biology and other natural sciences (92-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1 Manifolds and cell complexes (57-XX) 1 Numerical analysis (65-XX) 1 Computer science (68-XX) 1 Mechanics of particles and systems (70-XX)

#### Citations contained in zbMATH

33 Publications have been cited 335 times in 238 Documents Cited by Year
The center and cyclicity problems. A computational algebra approach. Zbl 1192.34003
Romanovski, Valery G.; Shafer, Douglas S.
2009
The center problem on a center manifold in $$\mathbb{R}^{3}$$. Zbl 1259.34021
Edneral, Victor F.; Mahdi, Adam; Romanovski, Valery G.; Shafer, Douglas S.
2012
Integral invariants and limit sets of planar vector fields. Zbl 1092.34013
García, Isaac A.; Shafer, Douglas S.
2005
The $${1:-q}$$ resonant center problem for certain cubic Lotka-Volterra systems. Zbl 1365.34006
Chen, Xingwu; Giné, Jaume; Romanovski, Valery G.; Shafer, Douglas S.
2012
$$1: - 3$$ resonant centers on $$\mathbb{C}^2$$ with homogeneous cubic nonlinearities. Zbl 1165.34334
Hu, Zhaoping; Romanovski, Valery G.; Shafer, Douglas S.
2008
Bifurcation of limit cycles from quadratic centers. Zbl 0833.34029
Shafer, Douglas S.; Zegeling, André
1995
Separatrix and limit cycles of quadratic systems and Dulac’s theorem. Zbl 0522.58041
Chicone, Carmen; Shafer, Douglas S.
1983
Stability and periodic oscillations in the Moon-Rand systems. Zbl 1264.34059
Mahdi, Adam; Romanovski, Valery G.; Shafer, Douglas S.
2013
On the center problem for $$p:-q$$ resonant polynomial vector fields. Zbl 1163.34020
Romanovski, Valery G.; Shafer, Douglas S.
2008
Bifurcation of critical periods of polynomial systems. Zbl 1337.34032
Ferčec, Brigita; Levandovskyy, Viktor; Romanovski, Valery G.; Shafer, Douglas S.
2015
Centers on center manifolds in the Lü system. Zbl 1252.70046
Mahdi, Adam; Pessoa, Claudio; Shafer, Douglas S.
2011
Cyclicity of a class of polynomial nilpotent center singularities. Zbl 1336.37041
García, Isaac A.; Shafer, Douglas S.
2016
Multiple bifurcation in a predator-prey system with non-monotonic predator response. Zbl 0763.92011
Rothe, Franz; Shafer, Douglas S.
1992
The cyclicity of a cubic system with nonradical Bautin ideal. Zbl 1163.34019
Levandovskyy, Viktor; Romanovski, Valery G.; Shafer, Douglas S.
2009
Singularities of gradient vector-fields in $$R^ 3$$. Zbl 0468.58017
Shafer, Douglas S.
1983
Centers and limit cycles in polynomial systems of ordinary differential equations. Zbl 1383.34053
Romanovski, Valery G.; Shafer, Douglas S.
2016
Symbolic computation and the cyclicity problem for singularities. Zbl 1259.34002
Shafer, Douglas S.
2012
Structural stability and generic properties of planar polynomial vector fields. Zbl 0677.58029
Shafer, Douglas S.
1987
Structural stability of planar polynomial foliations. Zbl 1091.34031
Jarque, Xavier; Llibre, Jaume; Shafer, Douglas S.
2005
Topological conjugacy of singularities of vector fields. Zbl 0622.58036
Shafer, Douglas S.; Swanson, Richard C.; Walker, Russell B.
1986
Cyclicity of polynomial nondegenerate centers on center manifolds. Zbl 1434.37030
García, Isaac A.; Maza, Susanna; Shafer, Douglas S.
2018
Asymptotics and stability of the delayed Duffing equation. Zbl 1395.34079
Hill, David C.; Shafer, Douglas S.
2018
Properties of monodromic points on center manifolds in $$\mathbb R^3$$ via Lie symmetries. Zbl 1311.37036
García, Isaac A.; Maza, Susanna; Shafer, Douglas S.
2013
Time-reversibility in two-dimensional polynomial systems. Zbl 1110.34026
Romanovski, Valery G.; Shafer, Douglas S.
2005
Vertices of planar curves under the action of linear transformations. Zbl 1011.53002
Shafer, Douglas S.; Zegeling, André
2002
Any two quadratic cycles can be connected with a smooth arc. Zbl 0945.34019
Shafer, Douglas S.; Zegeling, André
2000
Shafer, D. S.
1993
Restrictions on the equivalence homeomorphism in stability of polynomial vector fields. Zbl 0664.58021
Dumortier, Freddy; Shafer, Douglas S.
1990
Structure and stability of gradient polynomial vector fields. Zbl 0661.58016
Shafer, Douglas S.
1990
Structurally stable quadratic foliations. Zbl 1170.34038
Jarque, Xavier; Llibre, Jaume; Shafer, Douglas S.
2008
A numerical approach to bifurcations from quadratic centers. Zbl 0860.65061
Shafer, Douglas S.; Wu, Xiaonan; Zegeling, André
1996
Quadratic Morse-Smale vector fields which are not structurally stable. Zbl 0504.58026
Chicone, Carmen; Shafer, Douglas S.
1982
Topological equivalence of gradient vectorfields. Zbl 0426.58015
Shafer, Douglas S.
1980
Cyclicity of polynomial nondegenerate centers on center manifolds. Zbl 1434.37030
García, Isaac A.; Maza, Susanna; Shafer, Douglas S.
2018
Asymptotics and stability of the delayed Duffing equation. Zbl 1395.34079
Hill, David C.; Shafer, Douglas S.
2018
Cyclicity of a class of polynomial nilpotent center singularities. Zbl 1336.37041
García, Isaac A.; Shafer, Douglas S.
2016
Centers and limit cycles in polynomial systems of ordinary differential equations. Zbl 1383.34053
Romanovski, Valery G.; Shafer, Douglas S.
2016
Bifurcation of critical periods of polynomial systems. Zbl 1337.34032
Ferčec, Brigita; Levandovskyy, Viktor; Romanovski, Valery G.; Shafer, Douglas S.
2015
Stability and periodic oscillations in the Moon-Rand systems. Zbl 1264.34059
Mahdi, Adam; Romanovski, Valery G.; Shafer, Douglas S.
2013
Properties of monodromic points on center manifolds in $$\mathbb R^3$$ via Lie symmetries. Zbl 1311.37036
García, Isaac A.; Maza, Susanna; Shafer, Douglas S.
2013
The center problem on a center manifold in $$\mathbb{R}^{3}$$. Zbl 1259.34021
Edneral, Victor F.; Mahdi, Adam; Romanovski, Valery G.; Shafer, Douglas S.
2012
The $${1:-q}$$ resonant center problem for certain cubic Lotka-Volterra systems. Zbl 1365.34006
Chen, Xingwu; Giné, Jaume; Romanovski, Valery G.; Shafer, Douglas S.
2012
Symbolic computation and the cyclicity problem for singularities. Zbl 1259.34002
Shafer, Douglas S.
2012
Centers on center manifolds in the Lü system. Zbl 1252.70046
Mahdi, Adam; Pessoa, Claudio; Shafer, Douglas S.
2011
The center and cyclicity problems. A computational algebra approach. Zbl 1192.34003
Romanovski, Valery G.; Shafer, Douglas S.
2009
The cyclicity of a cubic system with nonradical Bautin ideal. Zbl 1163.34019
Levandovskyy, Viktor; Romanovski, Valery G.; Shafer, Douglas S.
2009
$$1: - 3$$ resonant centers on $$\mathbb{C}^2$$ with homogeneous cubic nonlinearities. Zbl 1165.34334
Hu, Zhaoping; Romanovski, Valery G.; Shafer, Douglas S.
2008
On the center problem for $$p:-q$$ resonant polynomial vector fields. Zbl 1163.34020
Romanovski, Valery G.; Shafer, Douglas S.
2008
Structurally stable quadratic foliations. Zbl 1170.34038
Jarque, Xavier; Llibre, Jaume; Shafer, Douglas S.
2008
Integral invariants and limit sets of planar vector fields. Zbl 1092.34013
García, Isaac A.; Shafer, Douglas S.
2005
Structural stability of planar polynomial foliations. Zbl 1091.34031
Jarque, Xavier; Llibre, Jaume; Shafer, Douglas S.
2005
Time-reversibility in two-dimensional polynomial systems. Zbl 1110.34026
Romanovski, Valery G.; Shafer, Douglas S.
2005
Vertices of planar curves under the action of linear transformations. Zbl 1011.53002
Shafer, Douglas S.; Zegeling, André
2002
Any two quadratic cycles can be connected with a smooth arc. Zbl 0945.34019
Shafer, Douglas S.; Zegeling, André
2000
A numerical approach to bifurcations from quadratic centers. Zbl 0860.65061
Shafer, Douglas S.; Wu, Xiaonan; Zegeling, André
1996
Bifurcation of limit cycles from quadratic centers. Zbl 0833.34029
Shafer, Douglas S.; Zegeling, André
1995
Shafer, D. S.
1993
Multiple bifurcation in a predator-prey system with non-monotonic predator response. Zbl 0763.92011
Rothe, Franz; Shafer, Douglas S.
1992
Restrictions on the equivalence homeomorphism in stability of polynomial vector fields. Zbl 0664.58021
Dumortier, Freddy; Shafer, Douglas S.
1990
Structure and stability of gradient polynomial vector fields. Zbl 0661.58016
Shafer, Douglas S.
1990
Structural stability and generic properties of planar polynomial vector fields. Zbl 0677.58029
Shafer, Douglas S.
1987
Topological conjugacy of singularities of vector fields. Zbl 0622.58036
Shafer, Douglas S.; Swanson, Richard C.; Walker, Russell B.
1986
Separatrix and limit cycles of quadratic systems and Dulac’s theorem. Zbl 0522.58041
Chicone, Carmen; Shafer, Douglas S.
1983
Singularities of gradient vector-fields in $$R^ 3$$. Zbl 0468.58017
Shafer, Douglas S.
1983
Quadratic Morse-Smale vector fields which are not structurally stable. Zbl 0504.58026
Chicone, Carmen; Shafer, Douglas S.
1982
Topological equivalence of gradient vectorfields. Zbl 0426.58015
Shafer, Douglas S.
1980
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#### Cited by 215 Authors

 44 Romanovski, Valery G. 37 Giné, Jaume 22 García, Isaac A. 16 Algaba, Antonio 15 Llibre, Jaume 15 Shafer, Douglas S. 15 Zhang, Weinian 14 García, Cristóbal 13 Ferčec, Brigita 12 Han, Maoan 11 Huang, Wentao 11 Valls Anglés, Cláudia 10 Chen, Xingwu 10 Maza, Susanna 8 Oliveira, Regilene D. S. 7 Liu, Yirong 7 Zhang, Xiang 6 Reyes, Manuel 6 Torregrosa, Joan 5 Dukarić, Maša 5 Fernandes, Wilker 5 Li, Chengzhi 5 Wang, Qinlong 5 Yu, Zhiheng 4 Dumortier, Freddy 4 Edneral, Victor F. 4 Fuentes, Natalia 4 Grau, Maite 4 Mahdi, Adam 4 Mencinger, Matej 4 Zhang, Zhifen 4 Zhao, Yulin 3 Boussaada, Islam 3 Buică, Adriana 3 Chen, Yufu 3 Dong, Guangfeng 3 Du, Chaoxiong 3 Giacomini, Hector J. 3 Guo, Laigang 3 Hu, Zhaoping 3 Li, Weigu 3 Liu, Lingling 3 Perko, Lawrence M. 3 Sang, Bo 3 Tang, Yilei 3 Zegeling, André 2 Aybar, Orhan Ozgur 2 Aziz, Waleed 2 Bardet, Magali 2 Bonckaert, Patrick 2 Boros, Balázs 2 Bravo, José Luis 2 Čanić, Sunčica 2 Chicone, Carmen C. 2 Chouikha, A. Raouf 2 Feng, Jingjing 2 Ferragut, Antoni 2 Gamero, Estanislao 2 Gasull, Armengol 2 Hofbauer, Josef 2 Iliev, Iliya Dimov 2 Jarque, Xavier 2 Kooij, Robert E. 2 Levandovskyy, Viktor 2 Li, Feng 2 Li, Na 2 Liu, Changjian 2 Merino, Manuel 2 Müller, Stefan 2 Pessoa, Claudio 2 Rabanal, Roland 2 Regensburger, Georg 2 Rodríguez-Luis, Alejandro J. 2 Sánchez-Sánchez, Iván 2 Strelcyn, Jean-Marie 2 Tavares Camacho, Maria Isabel 2 Wu, Kuilin 2 Xia, Yonghui 2 Xiao, Dongmei 2 Yang, Jiazhong 2 Yang, Lu 2 Yu, Jiang 2 Yu, Pei 2 Yu, Pei 2 Zhang, Qi 2 Zhou, Yuqing 1 Aldazharova, Maira 1 Aldibekov, Tamasha M. 1 Al-saedi, Ahmed Eid Salem 1 Alvarez, María Jesus 1 Aranson, Samuil Khaĭmovich 1 Athanassopoulos, Konstantin 1 Aybar, Ilknur Kusbeyzi 1 Bamón, Rodrigo 1 Barge, Marcy M. 1 Boulier, François 1 Buzzi, Claudio Aguinaldo 1 Cai, Zhangshan 1 Chaoxiong, Du 1 Chavarriga, Javier ...and 115 more Authors
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#### Cited in 67 Serials

 37 Journal of Differential Equations 19 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 18 Journal of Mathematical Analysis and Applications 16 Applied Mathematics and Computation 10 Qualitative Theory of Dynamical Systems 8 Nonlinear Analysis. Real World Applications 7 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 6 Chaos, Solitons and Fractals 6 Journal of Symbolic Computation 6 Discrete and Continuous Dynamical Systems 6 Nonlinear Dynamics 5 Journal of Computational and Applied Mathematics 5 Applied Mathematics Letters 5 Journal of Dynamics and Differential Equations 5 Bulletin des Sciences Mathématiques 4 Proceedings of the American Mathematical Society 4 Communications on Pure and Applied Analysis 3 Programming and Computer Software 3 Acta Applicandae Mathematicae 3 Abstract and Applied Analysis 3 Journal of Applied Analysis and Computation 2 Computers & Mathematics with Applications 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Science in China. Series A 2 Communications in Nonlinear Science and Numerical Simulation 2 Journal of Nonlinear Mathematical Physics 2 Differential Equations 2 Dynamical Systems 2 Mediterranean Journal of Mathematics 2 Science China. Mathematics 1 Journal of Mathematical Biology 1 Mathematical Biosciences 1 Nonlinearity 1 Physics Letters. A 1 Rocky Mountain Journal of Mathematics 1 Bulletin of Mathematical Biology 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Publications Mathématiques 1 Journal of Economic Theory 1 Journal of Mathematical Economics 1 Mathematics and Computers in Simulation 1 Metroeconomica 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Results in Mathematics 1 Transactions of the American Mathematical Society 1 Ergodic Theory and Dynamical Systems 1 Chinese Annals of Mathematics. Series B 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Physica D 1 Acta Mathematicae Applicatae Sinica. English Series 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Bulletin of the American Mathematical Society. New Series 1 Journal of Nonlinear Science 1 Experimental Mathematics 1 Journal of Mathematical Sciences (New York) 1 Electronic Journal of Differential Equations (EJDE) 1 NoDEA. Nonlinear Differential Equations and Applications 1 Journal of Mathematical Chemistry 1 Open Systems & Information Dynamics 1 Chaos 1 Acta Mathematica Sinica. English Series 1 Differentsial’nye Uravneniya i Protsessy Upravleniya 1 Discrete and Continuous Dynamical Systems. Series B 1 Journal of Applied Mathematics 1 Advances in Difference Equations 1 Nonlinear Analysis. Theory, Methods & Applications 1 European Journal of Mathematics
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#### Cited in 24 Fields

 207 Ordinary differential equations (34-XX) 91 Dynamical systems and ergodic theory (37-XX) 16 Biology and other natural sciences (92-XX) 10 Computer science (68-XX) 8 Commutative algebra (13-XX) 8 Numerical analysis (65-XX) 4 Difference and functional equations (39-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 Real functions (26-XX) 3 Partial differential equations (35-XX) 3 Mechanics of particles and systems (70-XX) 3 Fluid mechanics (76-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Systems theory; control (93-XX) 2 Field theory and polynomials (12-XX) 2 Algebraic geometry (14-XX) 2 Operator theory (47-XX) 2 Optics, electromagnetic theory (78-XX) 1 General and overarching topics; collections (00-XX) 1 Functions of a complex variable (30-XX) 1 Functional analysis (46-XX) 1 General topology (54-XX) 1 Manifolds and cell complexes (57-XX) 1 Statistical mechanics, structure of matter (82-XX)