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 213 articles , 1 standard article )

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  1. Campbell, Sue Ann; Wang, Zhen: Phase models and clustering in networks of oscillators with delayed coupling (2018)
  2. Jackson, Mark; Chen-Charpentier, Benito M.: A model of biological control of plant virus propagation with delays (2018)
  3. Calleja, R.C.; Humphries, A.R.; Krauskopf, B.: Resonance phenomena in a scalar delay differential equation with two state-dependent delays (2017)
  4. Fenzi, Luca; Michiels, Wim: Robust stability optimization for linear delay systems in a probabilistic framework (2017)
  5. Hao, Pengmiao; Wang, Xuechen; Wei, Junjie: Global Hopf bifurcation of a population model with stage structure and strong Allee effect (2017)
  6. Huang, Zhenqi; Fan, Chuchu; Mitra, Sayan: Bounded invariant verification for time-delayed nonlinear networked dynamical systems (2017)
  7. Ingalls, Brian; Mincheva, Maya; Roussel, Marc R.: Parametric sensitivity analysis of oscillatory delay systems with an application to gene regulation (2017)
  8. Jackson, Mark; Chen-Charpentier, Benito M.: Modeling plant virus propagation with delays (2017)
  9. Mirzaev, Inom; Bortz, David M.: A numerical framework for computing steady states of structured population models and their stability (2017)
  10. Niu, Ben: Codimension-two bifurcations induce hysteresis behavior and multistabilities in delay-coupled Kuramoto oscillators (2017)
  11. Shu, Hongying; Wang, Lin; Wu, Jianhong: Bounded global Hopf branches for stage-structured differential equations with unimodal feedback (2017)
  12. 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)
  13. Vermiglio, Rossana: Polynomial chaos expansions for the stability analysis of uncertain delay differential equations (2017)
  14. Yanchuk, Serhiy; Giacomelli, Giovanni: Spatio-temporal phenomena in complex systems with time delays (2017)
  15. Zhang, Shu; Yuan, Yuan: The Filippov equilibrium and sliding motion in an Internet congestion control model (2017)
  16. Ashwin, Peter; Coombes, Stephen; Nicks, Rachel: Mathematical frameworks for oscillatory network dynamics in neuroscience (2016)
  17. Bel, A.; Reartes, W.; Torresi, A.: Bifurcations in delay differential equations: an algorithmic approach in frequency domain (2016)
  18. Breda, D.; Diekmann, O.; Gyllenberg, M.; Scarabel, F.; Vermiglio, R.: Pseudospectral discretization of nonlinear delay equations: new prospects for numerical bifurcation analysis (2016)
  19. Chen-Charpentier, Benito M.; Diakite, Ibrahim: A mathematical model of bone remodeling with delays (2016)
  20. Collera, Juancho A.: Symmetry-breaking bifurcations in laser systems with all-to-all coupling (2016)

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