MATCONT

MATCONT: Matlab software for bifurcation study of dynamical systems. The study of differential equations requires good and powerful mathematical software. Also, flexibility and extendibility of the package are important. However, most of the existing software all have their own way of specifying the system or are written in a relatively low-level programming language, so it is hard to extend it. In 2000, A. Riet started the implementation of a continuation toolbox in Matlab. The aim of this toolbox was to provide an interactive environment for the continuation and normal form analysis of dynamical systems. In 2002, the toolbox was extended and improved by W. Mestrom. This toolbox was the base of the toolbox we further developed and extended with a GUI and named MATCONT. It contains some features which were never implemented before: continuation of branch points in three parameters, the universal use of minimally extended systems, and the computation of normal form coefficients for bifurcations of limit cycles. The software is free for download at http://www.matcont.UGent.be.


References in zbMATH (referenced in 170 articles , 1 standard article )

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  1. Al-Hdaibat, B.; Govaerts, W.; Kuznetsov, Yu.A.; Meijer, H.G.E.: Initialization of homoclinic solutions near Bogdanov-Takens points: Lindstedt-Poincaré compared with regular perturbation method (2016)
  2. Ashwin, Peter; Coombes, Stephen; Nicks, Rachel: Mathematical frameworks for oscillatory network dynamics in neuroscience (2016)
  3. Boie, Sebastian; Kirk, Vivien; Sneyd, James; Wechselberger, Martin: Effects of quasi-steady-state reduction on biophysical models with oscillations (2016)
  4. Breda, D.; Diekmann, O.; Gyllenberg, M.; Scarabel, F.; Vermiglio, R.: Pseudospectral discretization of nonlinear delay equations: new prospects for numerical bifurcation analysis (2016)
  5. Buffoni, G.; Groppi, M.; Soresina, C.: Dynamics of predator-prey models with a strong Allee effect on the prey and predator-dependent trophic functions (2016)
  6. Luo, Jianfeng; Wang, Wendi; Chen, Hongyan; Fu, Rui: Bifurcations of a mathematical model for HIV dynamics (2016)
  7. Nicola, Wilten; Campbell, Sue Ann: Nonsmooth bifurcations of mean field systems of two-dimensional integrate and fire neurons (2016)
  8. Aguirre, Pablo: Bifurcations of two-dimensional global invariant manifolds near a noncentral saddle-node homoclinic orbit (2015)
  9. Bakri, Taoufik; Kuznetsov, Yuri A.; Verhulst, Ferdinand: Torus bifurcations in a mechanical system (2015)
  10. Feng, Xiaomei; Ruan, Shigui; Teng, Zhidong; Wang, Kai: Stability and backward bifurcation in a malaria transmission model with applications to the control of malaria in China (2015)
  11. Guckenheimer, John; Lizarraga, Ian: Shilnikov homoclinic bifurcation of mixed-mode oscillations (2015)
  12. Kuehn, Christian: Multiple time scale dynamics (2015)
  13. Kutafina, Ekaterina: Mixed mode oscillations in the Bonhoeffer-van der Pol oscillator with weak periodic perturbation (2015)
  14. Liu, Ping; Siettos, C.I.; Gear, C.W.; Kevrekidis, I.G.: Equation-free model reduction in agent-based computations: coarse-grained bifurcation and variable-free rare event analysis (2015)
  15. Medetov, Bekbolat; Weiß, R.Gregor; Zhanabaev, Zeinulla Zh.; Zaks, Michael A.: Numerically induced bursting in a set of coupled neuronal oscillators (2015)
  16. Meijer, Hil G.E.; Eissa, Tahra L.; Kiewiet, Bert; Neuman, Jeremy F.; Schevon, Catherine A.; Emerson, Ronald G.; Goodman, Robert R.; McKhann, Guy M.; Marcuccilli, Charles J.; Tryba, Andrew K.; Cowan, Jack D.; van Gils, Stephan A.; van Drongelen, Wim: Modeling focal epileptic activity in the Wilson-cowan model with depolarization block (2015)
  17. Merrison-Hort, Robert: Fireflies: new software for interactively exploring dynamical systems using GPU computing (2015)
  18. Net, M.; Sánchez, J.: Continuation of bifurcations of periodic orbits for large-scale systems (2015)
  19. Nicola, Wilten; Ly, Cheng; Campbell, Sue Ann: One-dimensional population density approaches to recurrently coupled networks of neurons with noise (2015)
  20. Revel, G.; Alonso, D.M.; Moiola, J.L.: A degenerate 2:3 resonant Hopf-Hopf bifurcation as organizing center of the dynamics: numerical semiglobal results (2015)

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