AUTO2000 swMATH ID: 4643 Software Authors: Eusebius Doedel, with contribution from: 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/ Programming Languages: Fortran Operating Systems: UNIX/Linux Dependencies: Fortran 90 compiler Related Software: HomCont; AUTO; MATCONT; Matlab; CL_MATCONT; XPPAUT; LOCBIF; COLSYS; pde2path; NBI; CONTENT; GitHub; COCO; DLMF; REDUCE; Mathematica; CAPD; wavetrain; IRAM; eigs Cited in: 52 Publications all top 5 Cited by 101 Authors 7 Govaerts, Willy J. F. 6 Kuznetsov, Yuri Alexandrovich 5 Dhooge, Annick 3 Barrio, Roberto 3 Blesa, Fernando 3 Engel, Harald 3 Freire Macías, Emilio 3 Galán-Vioque, Jorge 3 Muñoz-Almaraz, Francisco Javier 3 Vanderbauwhede, Andre L. 2 Bordyugov, Grigory 2 Doedel, Eusebius J. 2 Kumar, Ajeet 2 Meijer, Hil G. E. 2 Sautois, B. 2 Serrano, Sergio E. 2 Thiele, Uwe 2 Ubertini, Filippo 2 Wechselberger, Martin 1 Amdjadi, Faridon 1 Barton, David A. W. 1 Bick, Christian 1 Bilbao, Stefan 1 Bordiougov, Grigori 1 Bribesh, Fathi A. M. 1 Broomhead, David S. 1 Bunder, J. E. 1 Casciati, Fabio 1 Chatterjee, Anindya 1 Dahlem, Markus A. 1 Dellnitz, Michael 1 Dena, Ángeles 1 Dieci, Luca 1 Ducceschi, Michele 1 Ei, Shin-Ichiro 1 Faravelli, Lucia 1 Fischer, Nils 1 Flunkert, Valentin 1 Fraštia, Ľubor 1 Friedman, Mark J. 1 Galán, José 1 García-Vallejo, Daniel 1 Healey, Timothy J. 1 Hessel-von Molo, Mirko 1 Hommes, Cars H. 1 Horton, Caroline A. 1 Hövel, Philipp 1 Huang, Jicai 1 Hui, Chung-Yuen 1 Izuhara, Hirofumi 1 Jin, Zhen 1 Kehrt, Matthew 1 Kell, Douglas B. 1 Kevrekidis, Ioannis George 1 Klausmeier, Christopher A. 1 Kreusser, Lisa Maria 1 Kuznetsov, W. 1 Li, Bailian 1 Lu, Min 1 Lust, K. W. A. 1 Mackenzie, Todd 1 Manz, Niklas 1 Martens, Erik Andreas 1 McLachlan, Robert I. 1 Mehta, Prashant G. 1 Mimura, Masayasu 1 Mitry, John 1 Muldoon, Mark R. 1 Neild, Simon A. 1 Offen, Christian 1 Panaggio, Mark J. 1 Panchenko, Valentyn 1 Paszek, Pawel 1 Pokorný, Pavel 1 Poria, Swarup 1 Rademacher, Jens Diederich Michael 1 Rasmussen, Bryan 1 Renson, Ludovic 1 Roberts, Anthony John 1 Rodin, P. 1 Sahoo, Banshidhar 1 Sandstede, Björn 1 Scheel, Arnd 1 Schöll, Eckehard 1 Song, Lipeng 1 Steinbock, Oliver 1 Sun, Guiquan 1 Tao, Molei 1 Touzé, Cyril 1 Uldall Kristiansen, K. 1 van der Weide, Roy 1 Van Leemput, Pieter 1 Wagener, Florian 1 Wang, Yunjiao 1 Webb, Craig J. 1 Weckesser, Warren 1 White, Michael R. H. 1 Witting, Katrin 1 Yue, Hong 1 Zgliczyński, Piotr ...and 1 more Authors all top 5 Cited in 29 Serials 10 Physica D 3 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 3 Nonlinear Dynamics 2 Applied Mathematics and Computation 2 SIAM Journal on Scientific Computing 2 Chaos 2 SIAM Journal on Applied Dynamical Systems 2 Journal of Theoretical Biology 1 Acta Mechanica 1 Computers & Mathematics with Applications 1 Computer Methods in Applied Mechanics and Engineering 1 Journal of Computational Physics 1 Journal of Engineering Mathematics 1 Journal of Fluid Mechanics 1 Nonlinearity 1 Chaos, Solitons and Fractals 1 Journal of Computational and Applied Mathematics 1 Journal of Differential Equations 1 Celestial Mechanics and Dynamical Astronomy 1 Computational Economics 1 Physics of Fluids 1 Mathematical Problems in Engineering 1 Journal of Vibration and Control 1 Differential Equations and Dynamical Systems 1 Mathematical and Computer Modelling of Dynamical Systems 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Computational Management Science 1 The European Physical Journal B. Condensed Matter and Complex Systems 1 Journal of Computational Dynamics all top 5 Cited in 15 Fields 25 Dynamical systems and ergodic theory (37-XX) 16 Numerical analysis (65-XX) 15 Ordinary differential equations (34-XX) 12 Partial differential equations (35-XX) 10 Biology and other natural sciences (92-XX) 6 Mechanics of particles and systems (70-XX) 6 Mechanics of deformable solids (74-XX) 3 Fluid mechanics (76-XX) 2 Operator theory (47-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Probability theory and stochastic processes (60-XX) 1 Computer science (68-XX) 1 Operations research, mathematical programming (90-XX) 1 Systems theory; control (93-XX) Citations by Year