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.

References in zbMATH (referenced in 40 articles , 1 standard article )

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  1. 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)
  2. Li, Peng; Jiang, Ziwang: Bifurcation analysis of stick-slip motion of the vibration-driven system with dry friction (2018)
  3. Wang, Aili; Xiao, Yanni; Zhu, Huaiping: Dynamics of a Filippov epidemic model with limited hospital beds (2018)
  4. Páez Chávez, Joseph; Götz, Thomas; Siegmund, Stefan; Wijaya, Karunia Putra: An SIR-dengue transmission model with seasonal effects and impulsive control (2017)
  5. Páez Chávez, Joseph; Jungmann, Dirk; Siegmund, Stefan: Modeling and analysis of integrated pest control strategies via impulsive differential equations (2017)
  6. Simpson, David J. W.: Grazing-sliding bifurcations creating infinitely many attractors (2017)
  7. 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)
  8. Simpson, D. J. W.: Border-collision bifurcations in (\mathbbR^N) (2016)
  9. Efstathiou, Konstantinos; Liu, Xia; Broer, Henk W.: The boundary-Hopf-fold bifurcation in Filippov systems (2015)
  10. Tang, Guangyao; Qin, Wenjie; Tang, Sanyi: Complex dynamics and switching transients in periodically forced Filippov prey-predator system (2014)
  11. Amador, Jorge A.; Olivar, Gerard; Angulo, Fabiola: Smooth and Filippov models of sustainable development: bifurcations and numerical computations (2013)
  12. Buřič, Lubor; Janovský, Vladimír: Continuation of oscillatory patterns in a road traffic model of three cars (2012)
  13. Tang, Sanyi; Liang, Juhua; Xiao, Yanni; Cheke, Robert A.: Sliding bifurcations of Filippov two stage pest control models with economic thresholds (2012)
  14. Dercole, Fabio; Della Rossa, Fabio; Colombo, Alessandro; Kuznetsov, Yuri A.: Two degenerate boundary equilibrium bifurcations in planar Filippov systems (2011)
  15. Křivan, Vlastimil: On the Gause predator-prey model with a refuge: a fresh look at the history (2011)
  16. Meza, Magno Enrique Mendoza; da Silveira Costa, Michel Iskin: Exploitation of a single species by a threshold management policy (2011)
  17. Colombo, Alessandro; Dercole, Fabio: Discontinuity induced bifurcations of nonhyperbolic cycles in nonsmooth systems (2010)
  18. Guardia, Marcel; Hogan, S. John; Seara, Tere M.: An analytical approach to codimension-2 sliding bifurcations in the dry-friction oscillator (2010)
  19. Arango, Iván; Taborda, John Alexander: Integration-free analysis of nonsmooth local dynamics in planar Filippov systems (2009)
  20. Barton, David A. W.: Stability calculations for piecewise-smooth delay equations (2009)

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