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 333 articles , 1 standard article )

Showing results 1 to 20 of 333.
Sorted by year (citations)

1 2 3 ... 15 16 17 next

  1. Church, Kevin E. M.; Lessard, Jean-Philippe: Rigorous verification of Hopf bifurcations in functional differential equations of mixed type (2022)
  2. Gedeon, Tomáš; Humphries, Antony R.; Mackey, Michael C.; Walther, Hans-Otto; Wang, Zhao: Operon dynamics with state dependent transcription and/or translation delays (2022)
  3. Vörös, Illés; Takács, Dénes: Lane-keeping control of automated vehicles with feedback delay: nonlinear analysis and laboratory experiments (2022)
  4. Breda, Dimitri; Liessi, Davide: Floquet theory and stability of periodic solutions of renewal equations (2021)
  5. Chen, L.; Campbell, S. A.: Hysteresis bifurcation and application to delayed Fitzhugh-Nagumo neural systems (2021)
  6. Church, Kevin E. M.: Eigenvalues and delay differential equations: periodic coefficients, impulses and rigorous numerics (2021)
  7. de Wolff, B. A. J.; Scarabel, F.; Verduyn Lunel, S. M.; Diekmann, O.: Pseudospectral approximation of Hopf bifurcation for delay differential equations (2021)
  8. Gulbudak, Hayriye; Salceanu, Paul L.; Wolkowicz, Gail S. K.: A delay model for persistent viral infections in replicating cells (2021)
  9. Khristichenko, M. Yu.; Nechepurenko, Yu. M.: Computation of periodic solutions to models of infectious disease dynamics and immune response (2021)
  10. Oh, Sanghoon; Avedisov, Sergei S.; Orosz, Gábor: On the handling of automated vehicles: modeling, bifurcation analysis, and experiments (2021)
  11. Ramírez, Adrián; Breda, Dimitri; Sipahi, Rifat: A scalable approach to compute delay margin of a class of neutral-type time delay systems (2021)
  12. Rogov, Kirill; Pogromsky, Alexander; Steur, Erik; Michiels, Wim; Nijmeijer, Henk: Detecting coexisting oscillatory patterns in delay coupled Lur’e systems (2021)
  13. Scarabel, Francesca; Diekmann, Odo; Vermiglio, Rossana: Numerical bifurcation analysis of renewal equations via pseudospectral approximation (2021)
  14. Shi, Junping; Wang, Chuncheng; Wang, Hao: Spatial movement with diffusion and memory-based self-diffusion and cross-diffusion (2021)
  15. Song, Tianqi; Wang, Chuncheng; Tian, Boping: Multiple periodic solutions of a within-host malaria infection model with time delay (2021)
  16. Xu, Qi; Wang, Zaihua; Cheng, Li: Calculating characteristic roots of multi-delayed systems with accumulation points via a definite integral method (2021)
  17. 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)
  18. Abuthahir; Malangadan, Nizar; Raina, Gaurav: Effect of two forms of feedback on the performance of the rate control protocol (RCP) (2020)
  19. 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)
  20. Andò, Alessia; Breda, Dimitri: Convergence analysis of collocation methods for computing periodic solutions of retarded functional differential equations (2020)

1 2 3 ... 15 16 17 next

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