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 32 articles , 1 standard article )

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  1. 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)
  2. Simpson, D.J.W.: Border-collision bifurcations in $\mathbbR^N$ (2016)
  3. Efstathiou, Konstantinos; Liu, Xia; Broer, Henk W.: The boundary-Hopf-fold bifurcation in Filippov systems (2015)
  4. Amador, Jorge A.; Olivar, Gerard; Angulo, Fabiola: Smooth and Filippov models of sustainable development: bifurcations and numerical computations (2013)
  5. Buřič, Lubor; Janovský, Vladimír: Continuation of oscillatory patterns in a road traffic model of three cars (2012)
  6. Tang, Sanyi; Liang, Juhua; Xiao, Yanni; Cheke, Robert A.: Sliding bifurcations of Filippov two stage pest control models with economic thresholds (2012)
  7. Dercole, Fabio; Della Rossa, Fabio; Colombo, Alessandro; Kuznetsov, Yuri A.: Two degenerate boundary equilibrium bifurcations in planar Filippov systems (2011)
  8. Křivan, Vlastimil: On the Gause predator-prey model with a refuge: a fresh look at the history (2011)
  9. Meza, Magno Enrique Mendoza; da Silveira Costa, Michel Iskin: Exploitation of a single species by a threshold management policy (2011)
  10. Colombo, Alessandro; Dercole, Fabio: Discontinuity induced bifurcations of nonhyperbolic cycles in nonsmooth systems (2010)
  11. Guardia, Marcel; Hogan, S.John; Seara, Tere M.: An analytical approach to codimension-2 sliding bifurcations in the dry-friction oscillator (2010)
  12. Arango, Iván; Taborda, John Alexander: Integration-free analysis of nonsmooth local dynamics in planar Filippov systems (2009)
  13. Barton, David A.W.: Stability calculations for piecewise-smooth delay equations (2009)
  14. Buřič, Lubor; Janovský, Vladimír: The traffic problem: modeling of the overtaking (2009)
  15. Colombo, Alessandro; Lamiani, Paola; Benadero, Luis; di Bernardo, Mario: Two-parameter bifurcation analysis of the buck converter (2009)
  16. Nordmark, Arne B.; Piiroinen, Petri T.: Simulation and stability analysis of impacting systems with complete chattering (2009)
  17. da Silveira Costa, Michel Iskin: Predator harvesting in stage dependent predation models: insights from a threshold management policy (2008)
  18. di Bernardo, M.; Budd, C.J.; Champneys, A.R.; Kowalczyk, P.: Piecewise-smooth dynamical systems. Theory and applications (2008)
  19. Kowalczyk, P.; Piiroinen, P.T.: Two-parameter sliding bifurcations of periodic solutions in a dry-friction oscillator (2008)
  20. Piiroinen, Petri T.; Kuznetsov, Yuri A.: An event-driven method to simulate Filippov systems with accurate computing of sliding motions. (2008)

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