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; PITCON; LOCBIF; Maple; AUTO2000; COLSYS; CONTENT; COLNEW; SlideCont; Dynamics
Referenced in: 951 Publications
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Referenced by 1,415 Authors

35 Krauskopf, Bernd
27 Champneys, Alan R.
26 Osinga, Hinke Maria
23 Kooi, Bob W.
23 Yagasaki, Kazuyuki
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 Kevrekidis, Ioannis George
11 Qin, Bo-Wei
11 Sherratt, Jonathan A.
10 Bassom, Andrew P.
10 Chung, Kwok-Wai
10 Knobloch, Edgar
9 Desroches, Mathieu
9 Kirk, Vivien
9 Vo, Theodore
8 Friedman, Mark J.
8 Krupa, Martin
8 Merino, Manuel
8 van der Heijden, Gert H. M.
7 Aguirre, Pablo
7 Ajbar, Abdelhamid
7 Coman, Ciprian D.
7 Elnashaie, S. S. E. H.
7 Ghayesh, Mergen H.
7 Kühn, Christian
7 Laing, Carlo R.
7 Pavlou, Stavros
7 Rand, Richard H.
6 Aguiar, Maíra
6 Bertram, Richard
6 Collings, John B.
6 Dawes, Jonathan H. P.
6 Guckenheimer, John M.
6 Kalliadasis, Serafim
6 Meijer, Hil G. E.
6 Moehlis, Jeff
6 Neild, Simon A.
6 Oldeman, Bart E.
6 Páez Chávez, Joseph Nikolai
6 Ren, Jingli
6 Rucklidge, Alastair M.
6 Stollenwerk, Nico
6 Thiele, Uwe
6 van Veen, Lennaert
6 Wadee, M. Ahmer
6 Wadee, M. Khurram
6 Wake, Graeme Charles
6 Wechselberger, Martin
6 Wieczorek, Sebastian M.
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 Hill, Thomas L.
5 Horikawa, Yo
5 Izuhara, Hirofumi
5 Moiola, Jorge Luis
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
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 Frascoli, Federico
4 Garhyan, Parag
4 Glass, Leon
4 Harjanto, Eric
4 Healey, Timothy J.
4 Hogan, S. John
4 In, Visarath
4 Keller, Herbert Bishop
4 Kuwamura, Masataka
4 Langfield, Peter
4 Lord, Gabriel James
4 Mahecha-Botero, Andrés
4 Maini, Philip Kumar
4 McLachlan, Robert I.
4 Mehta, Prashant G.
...and 1,315 more Authors
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Referenced in 162 Serials

118 Physica D
51 SIAM Journal on Applied Dynamical Systems
49 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
46 Nonlinear Dynamics
29 Journal of Mathematical Biology
29 Mathematical Biosciences
25 Journal of Theoretical Biology
24 Communications in Nonlinear Science and Numerical Simulation
21 Bulletin of Mathematical Biology
20 Chaos, Solitons and Fractals
20 Chaos
18 Nonlinearity
18 Mathematical and Computer Modelling
17 Journal of Nonlinear Science
14 Journal of Computational Physics
13 Applied Mathematics and Computation
13 Journal of Computational and Applied Mathematics
12 Physics Letters. A
12 Theoretical Population Biology
12 SIAM Journal on Applied Mathematics
10 Acta Mechanica
10 Biological Cybernetics
10 Computer Methods in Applied Mechanics and Engineering
9 Journal of Engineering Mathematics
9 Journal of Fluid Mechanics
9 Journal of the Mechanics and Physics of Solids
8 The Journal of Mathematical Neuroscience
7 Dynamical Systems
7 Journal of Computational Dynamics
6 International Journal of Engineering Science
6 ACM Transactions on Mathematical Software
6 Meccanica
6 Dynamics and Stability of Systems
6 Applied Mathematical Modelling
6 SIAM Journal on Scientific Computing
6 Discrete and Continuous Dynamical Systems. Series B
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 Journal of Differential Equations
5 Applied Mathematics Letters
5 Japan Journal of Industrial and Applied Mathematics
5 Journal of Dynamics and Differential Equations
5 Nonlinear Analysis. Real World Applications
5 Mathematical Modelling of Natural Phenomena
5 Discrete and Continuous Dynamical Systems. Series S
4 Journal of the Franklin Institute
4 Mathematics and Computers in Simulation
4 Applied Numerical Mathematics
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 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 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 International Journal of Structural Stability and Dynamics
2 Applicable Analysis
2 Archive for Rational Mechanics and Analysis
2 Mathematical Methods in the Applied Sciences
2 Mathematics of Computation
2 Automatica
2 International Journal for Numerical Methods in Engineering
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 International Journal of Computer Mathematics
2 Journal of Elasticity
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 New Journal of Physics
2 European Journal of Mechanics. A. Solids
2 Qualitative Theory of Dynamical Systems
2 Sādhanā
2 Mathematical Biosciences and Engineering
2 Communications in Computational Physics
1 Artificial Intelligence
1 Computers and Fluids
1 Geophysical and Astrophysical Fluid Dynamics
1 IMA Journal of Applied Mathematics
1 IMA Journal of Numerical Analysis
...and 62 more Serials
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Referenced in 36 Fields

359 Dynamical systems and ergodic theory (37-XX)
358 Ordinary differential equations (34-XX)
292 Biology and other natural sciences (92-XX)
204 Numerical analysis (65-XX)
167 Partial differential equations (35-XX)
100 Mechanics of deformable solids (74-XX)
96 Mechanics of particles and systems (70-XX)
92 Fluid mechanics (76-XX)
30 Systems theory; control (93-XX)
27 Optics, electromagnetic theory (78-XX)
24 Statistical mechanics, structure of matter (82-XX)
22 Classical thermodynamics, heat transfer (80-XX)
19 Computer science (68-XX)
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7 Operator theory (47-XX)
7 Operations research, mathematical programming (90-XX)
6 Integral equations (45-XX)
6 Information and communication theory, circuits (94-XX)
5 Quantum theory (81-XX)
3 Combinatorics (05-XX)
3 Difference and functional equations (39-XX)
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