SLIDECONT, an AUTO97 driver for sliding bifurcation analysis of discontinuous piecewise-smooth autonomous systems, known as Filippov systems, is described in detail. Sliding bifurcations are those in which some sliding on the discontinuity boundary is critically involved. The software allows for detection and continuation of codimension $-1$ sliding bifurcations as well as detection of some codimension $-2$ singularities, with special attention to planar systems $(n=2)$. Some bifurcations are also supported for $n$-dimensional systems. This article gives a brief introduction to Filippov systems, describes the structure of SLIDECONT and all computations supported by SLIDECONT 2.0. Several examples, which are distributed together with the source code of SLIDECONT, are presented.

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  1. Bolzoni, Luca; Marca, Rossella Della; Groppi, Maria; Gragnani, Alessandra: Dynamics of a metapopulation epidemic model with localized culling (2020)
  2. Páez Chávez, Joseph; Zhang, Zhi; Liu, Yang: A numerical approach for the bifurcation analysis of nonsmooth delay equations (2020)
  3. Camara, B. I.; Yamapi, R.; Mokrani, H.: Environmental stochastic effects on phytoplankton-zooplankton dynamics (2019)
  4. Chávez, Joseph Páez; Gürbüz, Burcu; Pinto, Carla M. A.: The effect of aggressive chemotherapy in a model for HIV/AIDS-cancer dynamics (2019)
  5. Colombo, Alessandro; Del Buono, Nicoletta; Lopez, Luciano; Pugliese, Alessandro: Computational techniques to locate crossing/sliding regions and their sets of attraction in non-smooth dynamical systems (2018)
  6. Li, Peng; Jiang, Ziwang: Bifurcation analysis of stick-slip motion of the vibration-driven system with dry friction (2018)
  7. Páez Chávez, Joseph; Jungmann, Dirk; Siegmund, Stefan: A comparative study of integrated pest management strategies based on impulsive control (2018)
  8. Wang, Aili; Xiao, Yanni; Zhu, Huaiping: Dynamics of a Filippov epidemic model with limited hospital beds (2018)
  9. Páez Chávez, Joseph; Götz, Thomas; Siegmund, Stefan; Wijaya, Karunia Putra: An SIR-dengue transmission model with seasonal effects and impulsive control (2017)
  10. Páez Chávez, Joseph; Jungmann, Dirk; Siegmund, Stefan: Modeling and analysis of integrated pest control strategies via impulsive differential equations (2017)
  11. Simpson, David J. W.: Grazing-sliding bifurcations creating infinitely many attractors (2017)
  12. Bizzarri, Federico; Colombo, Alessandro; Dercole, Fabio; Gajani, Giancarlo Storti: Necessary and sufficient conditions for the noninvertibility of fundamental solution matrices of a discontinuous system (2016)
  13. Simpson, D. J. W.: Border-collision bifurcations in (\mathbbR^N) (2016)
  14. Efstathiou, Konstantinos; Liu, Xia; Broer, Henk W.: The boundary-Hopf-fold bifurcation in Filippov systems (2015)
  15. Tang, Guangyao; Qin, Wenjie; Tang, Sanyi: Complex dynamics and switching transients in periodically forced Filippov prey-predator system (2014)
  16. Amador, Jorge A.; Olivar, Gerard; Angulo, Fabiola: Smooth and Filippov models of sustainable development: bifurcations and numerical computations (2013)
  17. Buřič, Lubor; Janovský, Vladimír: Continuation of oscillatory patterns in a road traffic model of three cars (2012)
  18. Tang, Sanyi; Liang, Juhua; Xiao, Yanni; Cheke, Robert A.: Sliding bifurcations of Filippov two stage pest control models with economic thresholds (2012)
  19. Dercole, Fabio; Della Rossa, Fabio; Colombo, Alessandro; Kuznetsov, Yuri A.: Two degenerate boundary equilibrium bifurcations in planar Filippov systems (2011)
  20. Křivan, Vlastimil: On the Gause predator-prey model with a refuge: a fresh look at the history (2011)

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