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 311 articles , 1 standard article )

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  1. Chen, L.; Campbell, S. A.: Hysteresis bifurcation and application to delayed Fitzhugh-Nagumo neural systems (2021)
  2. Ramírez, Adrián; Breda, Dimitri; Sipahi, Rifat: A scalable approach to compute delay margin of a class of neutral-type time delay systems (2021)
  3. Abuthahir; Malangadan, Nizar; Raina, Gaurav: Effect of two forms of feedback on the performance of the rate control protocol (RCP) (2020)
  4. 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)
  5. Andò, Alessia; Breda, Dimitri: Convergence analysis of collocation methods for computing periodic solutions of retarded functional differential equations (2020)
  6. Avitabile, Daniele; Desroches, Mathieu; Veltz, Romain; Wechselberger, Martin: Local theory for spatio-temporal canards and delayed bifurcations (2020)
  7. Beri, B.; Stepan, G.: Essential chaotic dynamics of chatter in turning processes (2020)
  8. Bosschaert, Maikel M.; Janssens, Sebastiaan G.; Kuznetsov, Yu. A.: Switching to nonhyperbolic cycles from codimension two bifurcations of equilibria of delay differential equations (2020)
  9. Diekmann, Odo; Scarabel, Francesca; Vermiglio, Rossana: Pseudospectral discretization of delay differential equations in sun-star formulation: results and conjectures (2020)
  10. Michiels, Wim; Fenzi, Luca: Spectrum-based stability analysis and stabilization of time-periodic time-delay systems (2020)
  11. Munsberg, L.; Javaloyes, J.; Gurevich, S. V.: Topological localized states in the time delayed Adler model: bifurcation analysis and interaction law (2020)
  12. Nechepurenko, Yuri; Khristichenko, Michael; Grebennikov, Dmitry; Bocharov, Gennady: Bistability analysis of virus infection models with time delays (2020)
  13. Páez Chávez, Joseph; Zhang, Zhi; Liu, Yang: A numerical approach for the bifurcation analysis of nonsmooth delay equations (2020)
  14. Pei, Lijun; Chen, Yameng; Wang, Shuo: Complicated oscillations and non-resonant double Hopf bifurcation of multiple feedback delayed control system of the gut microbiota (2020)
  15. Randall, E. Benjamin; Randolph, Nicholas Z.; Olufsen, Mette S.: Persistent instability in a nonhomogeneous delay differential equation system of the Valsalva maneuver (2020)
  16. Shu, Hongying; Xu, Wanxiao; Wang, Xiang-Sheng; Wu, Jianhong: Complex dynamics in a delay differential equation with two delays in tick growth with diapause (2020)
  17. Słowiński, Piotr; Al-Ramadhani, Sohaib; Tsaneva-Atanasova, Krasimira: Neurologically motivated coupling functions in models of motor coordination (2020)
  18. Chong, Ket Hing; Samarasinghe, Sandhya; Kulasiri, Don; Zheng, Jie: Mathematical modelling of core regulatory mechanism in p53 protein that activates apoptotic switch (2019)
  19. Church, Kevin E. M.; Liu, Xinzhi: Cost-effective robust stabilization and bifurcation suppression (2019)
  20. Collera, Juancho A.: Numerical continuation and bifurcation analysis in a harvested predator-prey model with time delay using DDE-biftool (2019)

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