Characteristic point sequences in local and global bifurcation analysis of Filippov systems

Abstract

We explain the set of rules behind of the LabView toolbox for bifurcation analysis of Filippov systems denominated SPTCont 1.0. This software can detect nonsmooth bifurcations in n-dimensional systems using integration-free algorithms based on the evaluation of the vector fields on the discontinuity boundary (DB). In this paper, we present the characteristic point sequences that the software detects to guarantee the existence of local and global nonsmooth bifurcations in planar Filippov systems (n = 2). These sequences can be extended to three-dimensional or higher dimension Filippov systems. Boolean-valued functions are used to formulate the conditions of existence for each point defined in the sequences. Dynamics on DB and cycles are defined in function of the set of points. The full catalog of codim 1 local and global bifurcations is used to define the characteristic point sequence when the bifurcation parameter is varied. Finally, an illustrative example is analyzed using step-by-step routines of SPTCont 1.0.