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 288 articles , 1 standard article )

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  1. Beri, B.; Stepan, G.: Essential chaotic dynamics of chatter in turning processes (2020)
  2. Bosschaert, Maikel M.; Janssens, Sebastiaan G.; Kuznetsov, Yu. A.: Switching to nonhyperbolic cycles from codimension two bifurcations of equilibria of delay differential equations (2020)
  3. 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)
  4. Randall, E. Benjamin; Randolph, Nicholas Z.; Olufsen, Mette S.: Persistent instability in a nonhomogeneous delay differential equation system of the Valsalva maneuver (2020)
  5. Słowiński, Piotr; Al-Ramadhani, Sohaib; Tsaneva-Atanasova, Krasimira: Neurologically motivated coupling functions in models of motor coordination (2020)
  6. Chong, Ket Hing; Samarasinghe, Sandhya; Kulasiri, Don; Zheng, Jie: Mathematical modelling of core regulatory mechanism in p53 protein that activates apoptotic switch (2019)
  7. Church, Kevin E. M.; Liu, Xinzhi: Cost-effective robust stabilization and bifurcation suppression (2019)
  8. Collera, Juancho A.: Numerical continuation and bifurcation analysis in a harvested predator-prey model with time delay using DDE-biftool (2019)
  9. De Souza, Daniel C.; Humphries, A. R.: Dynamics of a mathematical hematopoietic stem-cell population model (2019)
  10. 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)
  11. Guillot, Louis; Cochelin, Bruno; Vergez, Christophe: A Taylor series-based continuation method for solutions of dynamical systems (2019)
  12. 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)
  13. Guo, Yuxiao; Ji, Nannan; Niu, Ben: Hopf bifurcation analysis in a predator-prey model with time delay and food subsidies (2019)
  14. Guo, Yuxiao; Niu, Ben; Tian, Jianjun Paul: Backward Hopf bifurcation in a mathematical model for oncolytic virotherapy with the infection delay and innate immune effects (2019)
  15. Itovich, Griselda R.; Gentile, Franco S.; Moiola, Jorge L.: Hybrid methods for studying stability and bifurcations in delayed feedback systems (2019)
  16. Kiss, Adam K.; Avedisov, Sergei S.; Bachrathy, Daniel; Orosz, Gábor: On the global dynamics of connected vehicle systems (2019)
  17. Kunze, Tim; Haueisen, Jens; Knösche, Thomas R.: Emergence of cognitive priming and structure building from the hierarchical interaction of canonical microcircuit models (2019)
  18. Liu, Qingsong; Zhou, Bin: Regulation of linear systems with both pointwise and distributed input delays by memoryless feedback (2019)
  19. Li, Xu-Guang; Niculescu, Silviu-Iulian; Çela, Arben; Zhang, Lu: Stability analysis of uniformly distributed delay systems: a frequency-sweeping approach (2019)
  20. 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)

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