Abstract
Several models in the applied sciences are characterized by instantaneous changes in the solutions or discontinuities in the vector field. Knowledge of the geometry of interaction of the flow with the discontinuities can give new insights on the behaviour of such systems. Here, we focus on the class of the piecewise smooth systems of Filippov type. We describe some numerical techniques to locate crossing and sliding regions on the discontinuity surface, to compute the sets of attraction of these regions together with the mathematical form of the separatrices of such sets. Some numerical tests will illustrate our approach.
Highlights
Many nonsmooth dynamical systems can be described by piecewise smooth (PWS) systems of ordinary differential equations (ODEs), whose theory has been extensively described in [28]
Herebelow we summarize the main advantages of the 2D continuation method: 1. Stepsize is chosen adaptively based on the corrector’s length, so that the selection of points of S1 is influenced by the local curvature of the manifold rather than by the dynamics of the PWS system; 2
In this paper we proposed some computational approaches to approximate the sets of attraction for the crossing/sliding regions of a nonsmooth dynamical system of Filippov type
Summary
Many nonsmooth dynamical systems can be described by piecewise smooth (PWS) systems of ordinary differential equations (ODEs), whose theory has been extensively described in [28]. Interpolation or continuation methods can be useful to numerically compute separatrices of sets of attraction for the crossing/sliding regions.
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