DDE-BIFTOOL

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.


References in zbMATH (referenced in 184 articles , 1 standard article )

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  1. Jackson, Mark; Chen-Charpentier, Benito M.: Modeling plant virus propagation with delays (2017)
  2. Mirzaev, Inom; Bortz, David M.: A numerical framework for computing steady states of structured population models and their stability (2017)
  3. Shu, Hongying; Wang, Lin; Wu, Jianhong: Bounded global Hopf branches for stage-structured differential equations with unimodal feedback (2017)
  4. Terrien, Soizic; Krauskopf, Bernd; Broderick, Neil G.R.: Bifurcation analysis of the Yamada model for a pulsing semiconductor laser with saturable absorber and delayed optical feedback (2017)
  5. Vermiglio, Rossana: Polynomial chaos expansions for the stability analysis of uncertain delay differential equations (2017)
  6. Zhang, Shu; Yuan, Yuan: The Filippov equilibrium and sliding motion in an Internet congestion control model (2017)
  7. Ashwin, Peter; Coombes, Stephen; Nicks, Rachel: Mathematical frameworks for oscillatory network dynamics in neuroscience (2016)
  8. Breda, D.; Diekmann, O.; Gyllenberg, M.; Scarabel, F.; Vermiglio, R.: Pseudospectral discretization of nonlinear delay equations: new prospects for numerical bifurcation analysis (2016)
  9. Chen-Charpentier, Benito M.; Diakite, Ibrahim: A mathematical model of bone remodeling with delays (2016)
  10. Collera, Juancho A.: Symmetry-breaking bifurcations in laser systems with all-to-all coupling (2016)
  11. Gao, Qingbin; Olgac, Nejat: Bounds of imaginary spectra of LTI systems in the domain of two of the multiple time delays (2016)
  12. Gomez, Marcella M.; Sadeghpour, Mehdi; Bennett, Matthew R.; Orosz, Gábor; Murray, Richard M.: Stability of systems with stochastic delays and applications to genetic regulatory networks (2016)
  13. Humphries, A.R.; Bernucci, D.A.; Calleja, R.C.; Homayounfar, N.; Snarski, M.: Periodic solutions of a singularly perturbed delay differential equation with two state-dependent delays (2016)
  14. Keane, Andrew; Krauskopf, Bernd; Postlethwaite, Claire: Investigating irregular behavior in a model for the El Niño southern oscillation with positive and negative delayed feedback (2016)
  15. Krupa, Maciej; Touboul, Jonathan D.: Complex oscillations in the delayed Fitzhugh-Nagumo equation (2016)
  16. Li, Zhao-Yan; Zheng, Cong; Wang, Yong: Exponential stability analysis of integral delay systems with multiple exponential kernels (2016)
  17. Obando, Germán; Poveda, Jorge I.; Quijano, Nicanor: Replicator dynamics under perturbations and time delays (2016)
  18. Buono, Pietro-Luciano; Collera, Juancho A.: Symmetry-breaking bifurcations in rings of delay-coupled semiconductor lasers (2015)
  19. Chong, Ket Hing; Samarasinghe, Sandhya; Kulasiri, Don: Mathematical modelling of p53 basal dynamics and DNA damage response (2015)
  20. Dong, Yueping; Huang, Gang; Miyazaki, Rinko; Takeuchi, Yasuhiro: Dynamics in a tumor immune system with time delays (2015)

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Further publications can be found at: http://twr.cs.kuleuven.be/research/software/delay/delay_methods_publications.shtml