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AUTO

swMATH ID: 1059
Software Authors: Doedel, Eusebius, Alan Champneys, Fabio Dercole, Thomas Fairgrieve, Yuri Kuznetsov, Bart Oldeman, Randy Paffenroth, Bjorn Sandstede, Xianjun Wang, and Chenghai Zhang
Description: AUTO is a software for continuation and bifurcation problems in ordinary differential equations, originally developed by Eusebius Doedel, with subsequent major contribution by several people, including Alan Champneys, Fabio Dercole, Thomas Fairgrieve, Yuri Kuznetsov, Bart Oldeman, Randy Paffenroth, Bjorn Sandstede, Xianjun Wang, and Chenghai Zhang. AUTO can do a limited bifurcation analysis of algebraic systems of the form f(u,p) = 0, f,u in Rn and of systems of ordinary differential equations of the form u’(t) = f(u(t),p), f,u in Rn subject to initial conditions, boundary conditions, and integral constraints. Here p denotes one or more parameters. AUTO can also do certain continuation and evolution computations for parabolic PDEs. It also includes the software HOMCONT for the bifurcation analysis of homoclinic orbits. AUTO is quite fast and can benefit from multiple processors; therefore it is applicable to rather large systems of differential equations.
Homepage: http://indy.cs.concordia.ca/auto/
Keywords: aspects of the computer program AUTO; autonomous systems; free parameter; chemical reactions; population dynamics; steady state bifurcation point; Hopf bifurcation point; branch of steady states; branch of periodic solutions
Related Software: AUTO-07P; HomCont; AUTO-86; MATCONT; XPPAUT; Matlab; COCO; DDE-BIFTOOL; Mathematica; DSTool; CL_MATCONT; LOCBIF; PITCON; SlideCont; Maple; AUTO2000; CONTENT; COLSYS; TC-HAT; GitHub
Cited in: 1,016 Documents
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Cited by 1,525 Authors

39 Krauskopf, Bernd
29 Champneys, Alan R.
27 Osinga, Hinke Maria
26 Yagasaki, Kazuyuki
24 Kooi, Bob W.
22 Rodríguez-Luis, Alejandro J.
19 Algaba, Antonio
19 Doedel, Eusebius J.
14 Govaerts, Willy J. F.
14 Kuznetsov, Yuri Alexandrovich
12 Amabili, Marco
11 Desroches, Mathieu
11 Kevrekidis, Ioannis George
11 Qin, Bo-Wei
11 Sherratt, Jonathan A.
10 Bassom, Andrew P.
10 Chung, Kwok-Wai
10 Knobloch, Edgar
10 Vo, Theodore
9 Kirk, Vivien
9 Krupa, Martin
8 Aguirre, Pablo
8 Friedman, Mark J.
8 Merino, Manuel
8 Páez Chávez, Joseph Nikolai
8 van der Heijden, Gert H. M.
7 Aguiar, Maíra
7 Ajbar, Abdelhamid
7 Coman, Ciprian D.
7 Dawes, Jonathan H. P.
7 Elnashaie, S. S. E. H.
7 Ghayesh, Mergen H.
7 Izuhara, Hirofumi
7 Kühn, Christian
7 Laing, Carlo R.
7 Ogawa, Toshiyuki
7 Pavlou, Stavros
7 Rand, Richard H.
7 Sieber, Jan
7 Stollenwerk, Nico
7 Wieczorek, Sebastian M.
6 Bertram, Richard
6 Collings, John B.
6 Guckenheimer, John M.
6 Kalliadasis, Serafim
6 Meijer, Hil G. E.
6 Moehlis, Jeff
6 Neild, Simon A.
6 Oldeman, Bart E.
6 Rademacher, Jens Diederich Michael
6 Ren, Jingli
6 Rucklidge, Alastair M.
6 Thiele, Uwe
6 van Veen, Lennaert
6 Wadee, M. Ahmer
6 Wadee, M. Khurram
6 Wake, Graeme Charles
6 Wechselberger, Martin
5 Aronson, Donald G.
5 Audoly, Basile
5 Bär, Markus
5 Barrio, Roberto
5 Boer, Martin P.
5 Cammarano, Andrea
5 Dercole, Fabio
5 Farokhi, Hamed
5 Fernández-Sánchez, Fernando
5 Freire Macías, Emilio
5 Giraldo, Andrus
5 Healey, Timothy J.
5 Hill, Thomas L.
5 Horikawa, Yo
5 Moiola, Jorge Luis
5 Nelson, Mark Ian
5 Palacios, Antonio
5 Sandstede, Björn
5 Sneyd, James
5 Solís, Francisco Javier
5 Tseluiko, Dmitri
5 Wagenknecht, Thomas
5 Wanner, Thomas
5 Ward, Michael J.
5 Warmiński, Jerzy
5 Xu, Yancong
4 Al Saadi, Fahad
4 Alhumaizi, Khalid
4 Ashwin, Peter
4 Avitabile, Daniele
4 Bajaj, Anil K.
4 Balakrishnan, Easwaran
4 Chang, Yu
4 Coombes, Stephen
4 Dhooge, Annick
4 Ei, Shin-Ichiro
4 Ersöz, Elif Köksal
4 Frascoli, Federico
4 Gani, M. Osman
4 Garhyan, Parag
4 Glass, Leon
4 Harjanto, Eric
...and 1,425 more Authors
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Cited in 167 Serials

122 Physica D
56 SIAM Journal on Applied Dynamical Systems
51 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
50 Nonlinear Dynamics
31 Journal of Mathematical Biology
29 Mathematical Biosciences
27 Communications in Nonlinear Science and Numerical Simulation
25 Journal of Theoretical Biology
23 Bulletin of Mathematical Biology
22 Chaos, Solitons and Fractals
20 Nonlinearity
20 Journal of Nonlinear Science
20 Chaos
18 Mathematical and Computer Modelling
14 Journal of Computational Physics
13 Applied Mathematics and Computation
13 Journal of Computational and Applied Mathematics
12 Journal of Fluid Mechanics
12 Physics Letters. A
12 Theoretical Population Biology
12 SIAM Journal on Applied Mathematics
11 Biological Cybernetics
11 Computer Methods in Applied Mechanics and Engineering
11 Discrete and Continuous Dynamical Systems. Series B
10 Acta Mechanica
9 Journal of Engineering Mathematics
9 Journal of the Mechanics and Physics of Solids
8 The Journal of Mathematical Neuroscience
7 Meccanica
7 SIAM Journal on Scientific Computing
7 Dynamical Systems
7 Journal of Computational Dynamics
6 International Journal of Engineering Science
6 ACM Transactions on Mathematical Software
6 Journal of Differential Equations
6 Dynamics and Stability of Systems
6 Japan Journal of Industrial and Applied Mathematics
6 Applied Mathematical Modelling
6 Journal of Dynamics and Differential Equations
6 Discrete and Continuous Dynamical Systems. Series S
6 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
5 Computers & Mathematics with Applications
5 Computer Physics Communications
5 Applied Mathematics Letters
5 Nonlinear Analysis. Real World Applications
5 Mathematical Modelling of Natural Phenomena
4 Journal of the Franklin Institute
4 Mathematical Methods in the Applied Sciences
4 Mathematics and Computers in Simulation
4 Applied Numerical Mathematics
4 Journal of Elasticity
4 Celestial Mechanics and Dynamical Astronomy
4 Physics of Fluids
4 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
4 New Journal of Physics
4 Combustion Theory and Modelling
4 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
3 International Journal of Solids and Structures
3 Journal of Mathematical Analysis and Applications
3 Physics Reports
3 ZAMP. Zeitschrift für angewandte Mathematik und Physik
3 International Journal for Numerical Methods in Engineering
3 Neural Computation
3 Numerical Algorithms
3 Continuum Mechanics and Thermodynamics
3 Journal of Computational Neuroscience
3 European Journal of Mechanics. B. Fluids
3 Regular and Chaotic Dynamics
3 Qualitative Theory of Dynamical Systems
3 Mathematical Biosciences and Engineering
3 International Journal of Structural Stability and Dynamics
2 Applicable Analysis
2 Archive for Rational Mechanics and Analysis
2 Geophysical and Astrophysical Fluid Dynamics
2 Mathematics of Computation
2 Automatica
2 Numerische Mathematik
2 SIAM Journal on Numerical Analysis
2 Acta Applicandae Mathematicae
2 Acta Mathematicae Applicatae Sinica. English Series
2 Journal of Scientific Computing
2 European Journal of Applied Mathematics
2 International Journal of Computer Mathematics
2 Linear Algebra and its Applications
2 SIAM Review
2 Indagationes Mathematicae. New Series
2 Archive of Applied Mechanics
2 Calculus of Variations and Partial Differential Equations
2 Electronic Journal of Differential Equations (EJDE)
2 Advances in Computational Mathematics
2 Journal of Mathematical Chemistry
2 Mathematics and Mechanics of Solids
2 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
2 Discrete Dynamics in Nature and Society
2 European Journal of Mechanics. A. Solids
2 Sādhanā
2 Journal of Physics A: Mathematical and Theoretical
2 Communications in Computational Physics
1 Artificial Intelligence
1 Computers and Fluids
...and 67 more Serials
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Cited in 38 Fields

379 Dynamical systems and ergodic theory (37-XX)
378 Ordinary differential equations (34-XX)
314 Biology and other natural sciences (92-XX)
209 Numerical analysis (65-XX)
180 Partial differential equations (35-XX)
106 Mechanics of deformable solids (74-XX)
102 Mechanics of particles and systems (70-XX)
98 Fluid mechanics (76-XX)
33 Systems theory; control (93-XX)
27 Optics, electromagnetic theory (78-XX)
23 Computer science (68-XX)
23 Classical thermodynamics, heat transfer (80-XX)
23 Statistical mechanics, structure of matter (82-XX)
10 Calculus of variations and optimal control; optimization (49-XX)
10 Probability theory and stochastic processes (60-XX)
10 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
9 Geophysics (86-XX)
8 Information and communication theory, circuits (94-XX)
7 Operator theory (47-XX)
7 Operations research, mathematical programming (90-XX)
6 Integral equations (45-XX)
5 Quantum theory (81-XX)
3 Combinatorics (05-XX)
3 Difference and functional equations (39-XX)
3 Approximations and expansions (41-XX)
2 Linear and multilinear algebra; matrix theory (15-XX)
2 Global analysis, analysis on manifolds (58-XX)
2 Astronomy and astrophysics (85-XX)
1 General and overarching topics; collections (00-XX)
1 History and biography (01-XX)
1 Mathematical logic and foundations (03-XX)
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1 Potential theory (31-XX)
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1 Differential geometry (53-XX)
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1 Relativity and gravitational theory (83-XX)

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