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 326 articles , 1 standard article )

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  1. Breda, Dimitri; Liessi, Davide: Floquet theory and stability of periodic solutions of renewal equations (2021)
  2. Chen, L.; Campbell, S. A.: Hysteresis bifurcation and application to delayed Fitzhugh-Nagumo neural systems (2021)
  3. de Wolff, B. A. J.; Scarabel, F.; Verduyn Lunel, S. M.; Diekmann, O.: Pseudospectral approximation of Hopf bifurcation for delay differential equations (2021)
  4. Gulbudak, Hayriye; Salceanu, Paul L.; Wolkowicz, Gail S. K.: A delay model for persistent viral infections in replicating cells (2021)
  5. Khristichenko, M. Yu.; Nechepurenko, Yu. M.: Computation of periodic solutions to models of infectious disease dynamics and immune response (2021)
  6. Oh, Sanghoon; Avedisov, Sergei S.; Orosz, Gábor: On the handling of automated vehicles: modeling, bifurcation analysis, and experiments (2021)
  7. Ramírez, Adrián; Breda, Dimitri; Sipahi, Rifat: A scalable approach to compute delay margin of a class of neutral-type time delay systems (2021)
  8. Rogov, Kirill; Pogromsky, Alexander; Steur, Erik; Michiels, Wim; Nijmeijer, Henk: Detecting coexisting oscillatory patterns in delay coupled Lur’e systems (2021)
  9. Scarabel, Francesca; Diekmann, Odo; Vermiglio, Rossana: Numerical bifurcation analysis of renewal equations via pseudospectral approximation (2021)
  10. Xu, Qi; Wang, Zaihua; Cheng, Li: Calculating characteristic roots of multi-delayed systems with accumulation points via a definite integral method (2021)
  11. Zhang, Lu; Li, Xu-Guang; Mao, Zhi-Zhong; Chen, Jun-Xiu; Fan, Gao-Xia: Some new algebraic and geometric analysis for local stability crossing curves (2021)
  12. Abuthahir; Malangadan, Nizar; Raina, Gaurav: Effect of two forms of feedback on the performance of the rate control protocol (RCP) (2020)
  13. Aguirre-Hernández, Baltazar; Villafuerte-Segura, Raúl; Luviano-Juárez, Alberto; Loredo-Villalobos, Carlos Arturo; Díaz-González, Edgar Cristian: A panoramic sketch about the robust stability of time-delay systems and its applications (2020)
  14. Andò, Alessia; Breda, Dimitri: Convergence analysis of collocation methods for computing periodic solutions of retarded functional differential equations (2020)
  15. Avitabile, Daniele; Desroches, Mathieu; Veltz, Romain; Wechselberger, Martin: Local theory for spatio-temporal canards and delayed bifurcations (2020)
  16. Beri, B.; Stepan, G.: Essential chaotic dynamics of chatter in turning processes (2020)
  17. Bosschaert, Maikel M.; Janssens, Sebastiaan G.; Kuznetsov, Yu. A.: Switching to nonhyperbolic cycles from codimension two bifurcations of equilibria of delay differential equations (2020)
  18. Diekmann, Odo; Scarabel, Francesca; Vermiglio, Rossana: Pseudospectral discretization of delay differential equations in sun-star formulation: results and conjectures (2020)
  19. Gimeno, Joan; Jorba, Àngel: Using automatic differentiation to compute periodic orbits of delay differential equations (2020)
  20. Michiels, Wim; Fenzi, Luca: Spectrum-based stability analysis and stabilization of time-periodic time-delay systems (2020)

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