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 254 articles , 1 standard article )

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  1. Chong, Ket Hing; Samarasinghe, Sandhya; Kulasiri, Don; Zheng, Jie: Mathematical modelling of core regulatory mechanism in p53 protein that activates apoptotic switch (2019)
  2. Guo, Yuxiao; Ji, Nannan; Niu, Ben: Hopf bifurcation analysis in a predator-prey model with time delay and food subsidies (2019)
  3. 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)
  4. Várszegi, Balázs; Takács, Dénes; Orosz, Gábor: On the nonlinear dynamics of automated vehicles -- a nonholonomic approach (2019)
  5. Zhuge, Changjing; Mackey, Michael C.; Lei, Jinzhi: Origins of oscillation patterns in cyclical thrombocytopenia (2019)
  6. Breda, Dimitri; Liessi, Davide: Approximation of eigenvalues of evolution operators for linear renewal equations (2018)
  7. Campbell, Sue Ann; Wang, Zhen: Phase models and clustering in networks of oscillators with delayed coupling (2018)
  8. Elias Jarlebring, Max Bennedich, Giampaolo Mele, Emil Ringh, Parikshit Upadhyaya: NEP-PACK: A Julia package for nonlinear eigenproblems - v0.2 (2018) arXiv
  9. Hooton, Edward; Kravetc, Pavel; Rachinskii, Dmitrii: Restrictions to the use of time-delayed feedback control in symmetric settings (2018)
  10. Jackson, Mark; Chen-Charpentier, Benito M.: A model of biological control of plant virus propagation with delays (2018)
  11. Keane, A.; Krauskopf, B.: Chenciner bubbles and torus break-up in a periodically forced delay differential equation (2018)
  12. Li, Li; Xu, Jian: Bifurcation analysis and spatiotemporal patterns in unidirectionally delay-coupled vibratory gyroscopes (2018)
  13. Malygina, V. V.; Mulyukov, M. V.; Pertsev, N. V.: On local asymptotic stability of a model of epidemic process (2018)
  14. Pei, Lijun; Wu, Yangyang: Hopf bifurcation of the wireless network congestion model with state-dependent round trip delay (2018)
  15. Shu, Hongying; Chen, Yuming; Wang, Lin: Impacts of the cell-free and cell-to-cell infection modes on viral dynamics (2018)
  16. Song, Pengfei; Xiao, Yanni: Global Hopf bifurcation of a delayed equation describing the lag effect of media impact on the spread of infectious disease (2018)
  17. Unger, Benjamin: Discontinuity propagation in delay differential-algebraic equations (2018)
  18. Yucelen, Tansel; Yildiz, Yildiray; Sipahi, Rifat; Yousefi, Ehsan; Nguyen, Nhan: Stability limit of human-in-the-loop model reference adaptive control architectures (2018)
  19. Zhang, Shu; Yuan, Yuan; Xu, Jian: Model of a frame of dynamic routing and its equilibrium (2018)
  20. Balakin, Maksim Igor’evich; Ryskin, Nikita Mikhaĭlovich: Bifurcational mechanism of formation of developed multistability in a van der Pol oscillator with time-delayed feedback (2017)

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