DDE-BIFTOOL swMATH ID: 2396 Software Authors: Engelborghs, K.; Luzyanina, T.; Roose, D. Description: DDE-BIFTOOL is a Matlab package for numerical bifurcation and stability analysis of delay differential equations with several fixed discrete and/or state-dependent delays. It allows the computation, continuation and stability analysis of steady state solutions, their Hopf and fold bifurcations, periodic solutions and connecting orbits (but the latter only for the constant delay case). Stability analysis of steady state solutions is achieved through computing approximations and corrections to the rightmost characteristic roots. Periodic solutions, their Floquet multipliers and connecting orbits are computed using piecewise polynomial collocation on adaptively refined meshes. Homepage: http://twr.cs.kuleuven.be/research/software/delay/ddebiftool.shtml Dependencies: Matlab Keywords: DDE-BIFTOOL; Matlab package; periodic solutions; stability; Hopf bifurcations; delay differential equations; numerical bifurcation analysis Related Software: Matlab; AUTO; MATCONT; PDDE-CONT; Knut; XPPAUT; TRACE-DDE; dde23; GradSamp; HIFOO; COCO; HomCont; AUTO-07P; Maple; ARPACK; RADAR5; GitHub; PyDSTool; pde2path; LOCA Cited in: 356 Documents Further Publications: http://twr.cs.kuleuven.be/research/software/delay/delay_methods_publications.shtml Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year DDE-BIFTOOL, software for bifurcation analysis of delay differential equations: Functionality and applications. Zbl 1024.65509Engelborghs, K.; Luzyanina, T.; Roose, D. 2002 all top 5 Cited by 548 Authors 25 Michiels, Wim 20 Krauskopf, Bernd 16 Roose, Dirk 13 Breda, Dimitri 11 Engelborghs, Koen 11 Niculescu, Silviu-Iulian 10 Luzyanina, Tatyana 10 Stépán, Gábor 10 Vermiglio, Rossana 9 Shu, Hongying 9 Zhou, Bin 8 Campbell, Sue Ann 8 Green, Kirk 8 Orosz, Gábor 6 Pei, Lijun 6 Verheyden, Koen 6 Wei, Junjie 6 Xu, Jian 5 Carr, Thomas W. 5 Diekmann, Odo 5 Humphries, Antony R. 5 Kuznetsov, Yuri Alexandrovich 5 Lin, Zongli 5 Nijmeijer, Henk 5 Samaey, Giovanni 5 Scarabel, Francesca 5 Sipahi, Rifat 5 Steur, Erik 5 Wang, Lin 5 Wilson, Richard Eddie 4 Gökçe, Aytül 4 Guo, Yuxiao 4 Laing, Carlo R. 4 Li, Xuguang 4 Li, Zhaoyan 4 Mackey, Michael Charles 4 Maset, Stefano 4 Niu, Ben 4 Olgac, Nejat M. 4 Postlethwaite, Claire M. 4 Sieber, Jan 4 van Gils, Stephan A. 4 Wu, Jianhong 3 Barton, David A. W. 3 Bocharov, Gennady A. 3 Cela, Arben 3 Chen-Charpentier, Benito M. 3 Church, Kevin E. M. 3 Collera, Juancho A. 3 Dai, Qinrui 3 De Cesare, Luigi 3 Erneux, Thomas 3 Erzgräber, Hartmut 3 Gumussoy, Suat 3 Heckman, Christoffer R. 3 Hu, Haiyan 3 Insperger, Tamás 3 Janssens, Sebastiaan G. 3 Jarlebring, Elias 3 Keane, Andrew 3 Koopman, H. F. J. M. 3 Liessi, Davide 3 Rand, Richard H. 3 Sportelli, Mario C. 3 Takács, Dénes 3 van der Helm, Frans C. T. 3 Verdaasdonk, B. W. 3 Wagenknecht, Thomas 3 Wang, Chuncheng 3 Wang, Hao 3 Wang, Zaihua 3 Wolkowicz, Gail S. K. 3 Yuan, Yuan 3 Zhang, Li 3 Zhang, Shu 2 Amiranashvili, Shalva 2 Avedisov, Sergei S. 2 Bel, Andrea L. 2 Béri, Bence 2 Blyuss, Konstantin B. 2 Butcher, Eric A. 2 Cai, Tiaoyang 2 Calleja, Renato C. 2 Chen, Yuming 2 Chong, Ket Hing 2 Chung, Kwok-Wai 2 Cochelin, Bruno 2 Colijn, Caroline 2 Coombes, Stephen 2 Dombovari, Zoltan 2 Duan, Guangren 2 Duan, Shiming 2 Fenzi, Luca 2 Gentile, Franco Sebastián 2 Guillot, Louis 2 Gyllenberg, Mats 2 Hao, Pengmiao 2 Itovich, Griselda R. 2 Jackson, Mark G. 2 Janson, Natalia B. ...and 448 more Authors all top 5 Cited in 99 Serials 21 Physica D 20 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 17 SIAM Journal on Applied Dynamical Systems 14 Automatica 13 Journal of Computational and Applied Mathematics 12 Chaos 10 Journal of Mathematical Biology 10 Nonlinear Dynamics 9 Communications in Nonlinear Science and Numerical Simulation 8 Applied Mathematics and Computation 8 Discrete and Continuous Dynamical Systems. 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Mathematical, Physical and Engineering Sciences all top 5 Cited in 25 Fields 214 Ordinary differential equations (34-XX) 119 Biology and other natural sciences (92-XX) 86 Systems theory; control (93-XX) 85 Dynamical systems and ergodic theory (37-XX) 66 Numerical analysis (65-XX) 19 Partial differential equations (35-XX) 19 Mechanics of particles and systems (70-XX) 15 Optics, electromagnetic theory (78-XX) 10 Mechanics of deformable solids (74-XX) 8 Operations research, mathematical programming (90-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Fluid mechanics (76-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Integral equations (45-XX) 4 Probability theory and stochastic processes (60-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Operator theory (47-XX) 3 Computer science (68-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Quantum theory (81-XX) 2 Geophysics (86-XX) 1 General and overarching topics; collections (00-XX) 1 Special functions (33-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Global analysis, analysis on manifolds (58-XX) Citations by Year