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 232 articles , 1 standard article )

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  1. Breda, Dimitri; Liessi, Davide: Approximation of eigenvalues of evolution operators for linear renewal equations (2018)
  2. Campbell, Sue Ann; Wang, Zhen: Phase models and clustering in networks of oscillators with delayed coupling (2018)
  3. Hooton, Edward; Kravetc, Pavel; Rachinskii, Dmitrii: Restrictions to the use of time-delayed feedback control in symmetric settings (2018)
  4. Jackson, Mark; Chen-Charpentier, Benito M.: A model of biological control of plant virus propagation with delays (2018)
  5. Keane, A.; Krauskopf, B.: Chenciner bubbles and torus break-up in a periodically forced delay differential equation (2018)
  6. Li, Li; Xu, Jian: Bifurcation analysis and spatiotemporal patterns in unidirectionally delay-coupled vibratory gyroscopes (2018)
  7. Pei, Lijun; Wu, Yangyang: Hopf bifurcation of the wireless network congestion model with state-dependent round trip delay (2018)
  8. Song, Pengfei; Xiao, Yanni: Global Hopf bifurcation of a delayed equation describing the lag effect of media impact on the spread of infectious disease (2018)
  9. Zhang, Shu; Yuan, Yuan; Xu, Jian: Model of a frame of dynamic routing and its equilibrium (2018)
  10. Balakin, Maksim Igor’evich; Ryskin, Nikita Mikhaĭlovich: Bifurcational mechanism of formation of developed multistability in a van der Pol oscillator with time-delayed feedback (2017)
  11. Bauer, Larissa; Bassett, Jason; Hövel, Philipp; Kyrychko, Yuliya N.; Blyuss, Konstantin B.: Chimera states in multi-strain epidemic models with temporary immunity (2017)
  12. Calleja, R. C.; Humphries, A. R.; Krauskopf, B.: Resonance phenomena in a scalar delay differential equation with two state-dependent delays (2017)
  13. Fenzi, Luca; Michiels, Wim: Robust stability optimization for linear delay systems in a probabilistic framework (2017)
  14. Groothedde, C. M.; Mireles James, J. D.: Parameterization method for unstable manifolds of delay differential equations (2017)
  15. Hao, Pengmiao; Wang, Xuechen; Wei, Junjie: Global Hopf bifurcation of a population model with stage structure and strong Allee effect (2017)
  16. Huang, Zhenqi; Fan, Chuchu; Mitra, Sayan: Bounded invariant verification for time-delayed nonlinear networked dynamical systems (2017)
  17. Ingalls, Brian; Mincheva, Maya; Roussel, Marc R.: Parametric sensitivity analysis of oscillatory delay systems with an application to gene regulation (2017)
  18. Jackson, Mark; Chen-Charpentier, Benito M.: Modeling plant virus propagation with delays (2017)
  19. Mirzaev, Inom; Bortz, David M.: A numerical framework for computing steady states of structured population models and their stability (2017)
  20. Niu, Ben: Codimension-two bifurcations induce hysteresis behavior and multistabilities in delay-coupled Kuramoto oscillators (2017)

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