SlideCont: An Auto97 driver for bifurcation analysis of Filippov systems

ABSTRACT

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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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.7 Ordinary Differential Equations
          Subjects: Boundary value problems

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.0 General
          Subjects: Numerical algorithms

  J. Computer Applications
  J.2 PHYSICAL SCIENCES AND ENGINEERING
  J.3 LIFE AND MEDICAL SCIENCES

General Terms:
Algorithms

Keywords:
AUTO97, Filippov systems, numerical continuation, piecewise-smooth differential equations, sliding bifurcations