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 278 articles , 1 standard article )

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  1. Bosschaert, Maikel M.; Janssens, Sebastiaan G.; Kuznetsov, Yu. A.: Switching to nonhyperbolic cycles from codimension two bifurcations of equilibria of delay differential equations (2020)
  2. 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)
  3. Randall, E. Benjamin; Randolph, Nicholas Z.; Olufsen, Mette S.: Persistent instability in a nonhomogeneous delay differential equation system of the Valsalva maneuver (2020)
  4. Słowiński, Piotr; Al-Ramadhani, Sohaib; Tsaneva-Atanasova, Krasimira: Neurologically motivated coupling functions in models of motor coordination (2020)
  5. Chong, Ket Hing; Samarasinghe, Sandhya; Kulasiri, Don; Zheng, Jie: Mathematical modelling of core regulatory mechanism in p53 protein that activates apoptotic switch (2019)
  6. Church, Kevin E. M.; Liu, Xinzhi: Cost-effective robust stabilization and bifurcation suppression (2019)
  7. De Souza, Daniel C.; Humphries, A. R.: Dynamics of a mathematical hematopoietic stem-cell population model (2019)
  8. Getto, Philipp; Gyllenberg, Mats; Nakata, Yukihiko; Scarabel, Francesca: Stability analysis of a state-dependent delay differential equation for cell maturation: analytical and numerical methods (2019)
  9. Guillot, Louis; Cochelin, Bruno; Vergez, Christophe: A Taylor series-based continuation method for solutions of dynamical systems (2019)
  10. Guillot, Louis; Vergez, Christophe; Cochelin, Bruno: Continuation of periodic solutions of various types of delay differential equations using asymptotic numerical method and harmonic balance method (2019)
  11. Guo, Yuxiao; Ji, Nannan; Niu, Ben: Hopf bifurcation analysis in a predator-prey model with time delay and food subsidies (2019)
  12. Itovich, Griselda R.; Gentile, Franco S.; Moiola, Jorge L.: Hybrid methods for studying stability and bifurcations in delayed feedback systems (2019)
  13. Kunze, Tim; Haueisen, Jens; Knösche, Thomas R.: Emergence of cognitive priming and structure building from the hierarchical interaction of canonical microcircuit models (2019)
  14. Liu, Qingsong; Zhou, Bin: Regulation of linear systems with both pointwise and distributed input delays by memoryless feedback (2019)
  15. Martínez-González, A.; Méndez-Barrios, C.-F.; Niculescu, S.-I.; Chen, J.; Félix, L.: Weierstrass approach to asymptotic behavior characterization of critical imaginary roots for retarded differential equations (2019)
  16. Ma, Suqi: Hopf bifurcation of a type of neuron model with multiple time delays (2019)
  17. Pan, Xuejun; Chen, Yuming; Shu, Hongying: Rich dynamics in a delayed HTLV-I infection model: stability switch, multiple stable cycles, and torus (2019)
  18. Pei, Lijun; Wang, Shuo: Double Hopf bifurcation of differential equation with linearly state-dependent delays via MMS (2019)
  19. Pertsev, Nikolaĭ Viktorovich: Matrix stability and instability criteria for some systems of linear delay differential equations (2019)
  20. Scholl, T. H.; Gröll, L.; Hagenmeyer, V.: Time delay in the swing equation: a variety of bifurcations (2019)

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