AUTO swMATH ID: 1059 Software Authors: Doedel; Eusebius; Champneys, Alan; Dercole, Fabio; Fairgrieve, Thomas; Kuznetsov, Yuri; Oldeman, Bart; Paffenroth, Randy; Sandstede, Bjorn; Wang, Xianjun; Zhang, Chenghai 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; GitHub; CL_MATCONT; PITCON; LOCBIF; Maple; SlideCont; pde2path; AUTO2000; COLSYS; CONTENT Cited in: 1,071 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year AUTO: A program for the automatic bifurcation analysis of autonomous systems. Zbl 0511.65064Doedel, Eusebius 1981 all top 5 Cited by 1,604 Authors 40 Krauskopf, Bernd 30 Champneys, Alan R. 27 Osinga, Hinke Maria 27 Yagasaki, Kazuyuki 24 Kooi, Bob W. 22 Rodríguez-Luis, Alejandro J. 20 Doedel, Eusebius J. 19 Algaba, Antonio 15 Kuznetsov, Yuriĭ Aleksandrovich 14 Govaerts, Willy J. F. 14 Vo, Theodore 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 Kirk, Vivien 10 Knobloch, Edgar 10 Xu, Yancong 9 Krupa, Martin 9 van der Heijden, Gert H. M. 8 Aguirre, Pablo 8 Friedman, Mark J. 8 Horikawa, Yo 8 Kaper, Tasso J. 8 Merino, Manuel 8 Páez Chávez, Joseph Nikolai 7 Aguiar, Maíra 7 Ajbar, Abdelhamid 7 Barrio, Roberto 7 Bertram, Richard 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 Ren, Jingli 7 Sieber, Jan 7 Stollenwerk, Nico 7 Wieczorek, Sebastian M. 6 Al Saadi, Fahad 6 Collings, John B. 6 Giraldo, Andrus 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 Rong, Libin 6 Rucklidge, Alastair M. 6 Sneyd, James 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 Boer, Martin P. 5 Cammarano, Andrea 5 Dercole, Fabio 5 Farokhi, Hamed 5 Fernández-Sánchez, Fernando 5 Freire Macías, Emilio 5 Healey, Timothy J. 5 Hill, Thomas L. 5 Moiola, Jorge Luis 5 Nelson, Mark Ian 5 Palacios, Antonio 5 Perlikowski, Przemyslaw 5 Sandstede, Björn 5 Serrano, Sergio E. 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 Cisternas, Jaime E. 4 Coombes, Stephen 4 Dhooge, Annick 4 Ei, Shin-Ichiro 4 Ersöz, Elif Köksal ...and 1,504 more Authors all top 5 Cited in 171 Serials 124 Physica D 57 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 57 SIAM Journal on Applied Dynamical Systems 50 Nonlinear Dynamics 44 Chaos 31 Journal of Mathematical Biology 30 Mathematical Biosciences 27 Communications in Nonlinear Science and Numerical Simulation 25 Journal of Theoretical Biology 24 Bulletin of Mathematical Biology 22 Chaos, Solitons and Fractals 22 Journal of Nonlinear Science 21 Nonlinearity 18 Mathematical and Computer Modelling 14 Journal of Computational Physics 14 Journal of Fluid Mechanics 13 Applied Mathematics and Computation 13 Journal of Computational and Applied Mathematics 13 SIAM Journal on Applied Mathematics 12 Physics Letters. 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Solids 2 Sādhanā 2 Communications on Pure and Applied Analysis 2 Applied Mathematical Sciences 2 Journal of Physics A: Mathematical and Theoretical ...and 71 more Serials all top 5 Cited in 38 Fields 415 Ordinary differential equations (34-XX) 403 Dynamical systems and ergodic theory (37-XX) 333 Biology and other natural sciences (92-XX) 217 Numerical analysis (65-XX) 189 Partial differential equations (35-XX) 108 Mechanics of deformable solids (74-XX) 107 Mechanics of particles and systems (70-XX) 106 Fluid mechanics (76-XX) 34 Systems theory; control (93-XX) 27 Optics, electromagnetic theory (78-XX) 24 Computer science (68-XX) 23 Classical thermodynamics, heat transfer (80-XX) 23 Statistical mechanics, structure of matter (82-XX) 11 Probability theory and stochastic processes (60-XX) 10 Calculus of variations and optimal control; optimization (49-XX) 10 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 9 Geophysics (86-XX) 8 Operator theory (47-XX) 8 Operations research, mathematical programming (90-XX) 7 Integral equations (45-XX) 7 Information and communication theory, circuits (94-XX) 5 Quantum theory (81-XX) 4 Approximations and expansions (41-XX) 3 Combinatorics (05-XX) 3 Difference and functional equations (39-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 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Potential theory (31-XX) 1 Special functions (33-XX) 1 Functional analysis (46-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1 Relativity and gravitational theory (83-XX) Citations by Year