PDDE-CONT swMATH ID: 8419 Software Authors: Roose, Dirk; Szalai, Robert Description: Continuation and bifurcation analysis of delay differential equations This is a review article on numerical continuation and bifurcation analysis methods for delay differential equations (DDEs). The article is not meant as an introduction into the theory of DDEs or numerical methods for dynamical systems but it is ideal as an entry point for further reference. par Both authors are directly linked to the two currently freely available numerical packages for this purpose, PDDE-CONT and DDE-BIFTOOL. One author, R. Szalai, is the author and maintainer of PDDE-CONT, the other author, D. Roose, is the initiator (together with K. Engelborghs and T. Luzyanina) of DDE-BIFTOOL. The review discusses the numerical approaches implemented in PDDE-CONT and DDE-BIFTOOL for computation and stability analysis of equilibria and periodic orbits, and for continuing codimension-one bifurcations of equilibria and periodic orbits. par In its second part the review covers more specialist topics such as the computation and continuation of connecting orbits or quasi-periodic tori, and the treatment of neutral equations or state-dependent delays. The authors also discuss briefly, and refer to, related or alternative approaches by others (specifically, work by Breda and Barton). The paper is rounded off by several complex examples: a semiconductor laser with feedback (an example which has a continuous symmetry), a high-dimensional traffic model, a (regularized) nonsmooth model for chattering, and the classical Mackey-Glass equation. Homepage: https://gitorious.org/knut/pages/Home Keywords: delay differential equations; numerical continuation; bifurcation analysis Related Software: DDE-BIFTOOL; Knut; dde23; pchip; UNCMND; ARPACK; AUTO; Matlab; Taylor; dcc; COLSYS; TRACE-DDE; RODAS; RADAR5; LAPACK; JDQZ; AUTO-86; JDQR; HomCont; Dynamics Cited in: 31 Publications all top 5 Cited by 60 Authors 7 Krauskopf, Bernd 4 Orosz, Gábor 3 Keane, Andrew 3 Roose, Dirk 2 Avedisov, Sergei S. 2 Engelborghs, Koen 2 Humphries, Antony R. 2 Khristichenko, Michael Yu. 2 Lust, Kurt 2 Luzyanina, Tatyana 2 Nechepurenko, Yuri M. 2 Postlethwaite, Claire M. 1 Andò, Alessia 1 Baker, Christopher Thomas Hale 1 Balanov, Alexander G. 1 Bennett, Matthew R. 1 Bocharov, Gennady A. 1 Breda, Dimitri 1 Broderick, Neil G. R. 1 Calleja, Renato C. 1 Chung, Kwok-Wai 1 Coombes, Stephen 1 Deng, Shaojiang 1 Doedel, Eusebius J. 1 Dombovari, Zoltan 1 Ford, Neville J. 1 Gimeno, Joan 1 Gomez, Marcella M. 1 Grebennikov, Dmitry S. 1 Gröll, Lutz 1 Guo, Songtao 1 Hagenmeyer, Veit 1 Insperger, Tamás 1 Janson, Natalia B. 1 Jorba, Àngel 1 Liu, Defang 1 Mabonzo, Vital Delmas 1 Maset, Stefano 1 McClintock, Peter Vaughan Elsmere 1 Meijer, Hil G. E. 1 Molnar, Tamas G. 1 Murray, Richard M. 1 Olufsen, Mette Sofie 1 Randall, E. Benjamin 1 Randolph, Nicholas Z. 1 Ruschel, Stefan 1 Sadeghpour, Mehdi 1 Scholl, T. H. 1 Sieber, Jan 1 Słowiński, Piotr 1 Stépán, Gábor 1 Szalai, Róbert 1 Terrien, Soizic 1 Tucker, Robin W. 1 Verheyden, Koen 1 Wang, Charles H.-T. 1 Wieczorek, Sebastian M. 1 Wulf, Volker 1 Xu, Jian 1 Xu, Yingxiang all top 5 Cited in 19 Serials 5 SIAM Journal on Applied Dynamical Systems 3 Journal of Computational and Applied Mathematics 3 Discrete and Continuous Dynamical Systems. Series B 2 Chaos, Solitons and Fractals 2 Nonlinear Dynamics 1 Journal of the Franklin Institute 1 Journal of Mathematical Biology 1 Mathematical Biosciences 1 Nonlinearity 1 Applied Mathematics and Computation 1 BIT 1 Numerische Mathematik 1 SIAM Journal on Numerical Analysis 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Journal of Nonlinear Science 1 Russian Journal of Numerical Analysis and Mathematical Modelling 1 Chaos 1 Discrete and Continuous Dynamical Systems. Series S 1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences all top 5 Cited in 12 Fields 22 Ordinary differential equations (34-XX) 11 Dynamical systems and ergodic theory (37-XX) 11 Numerical analysis (65-XX) 6 Biology and other natural sciences (92-XX) 4 Systems theory; control (93-XX) 2 Optics, electromagnetic theory (78-XX) 2 Operations research, mathematical programming (90-XX) 1 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Mechanics of deformable solids (74-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Geophysics (86-XX) Citations by Year