Application of Hénon method in numerical estimation of the stick–slip transitions existing in Filippov-type discontinuous dynamical systems with dry friction

Accuracy of numerical modeling of any discontinuous dynamical system plays an important role in the proper use of the tools applied for its analysis. No less important in this matter is the numerical estimation of the phase trajectories, bifurcation diagrams, and Lyapunov exponents. This paper meets these expectations presenting application of Hénon’s method to obtain good numerical estimations of the stick–slip transitions existing in the Filippov-type discontinuous dynamical systems with dry friction. Subsequent sections are focused on the problem definition, block diagrams of the numerical procedure coded in Python, application of the method that was originally proposed for Poincaré maps, its use in estimation of phase trajectories, bifurcation diagrams of tangent points, and on estimation of the Lyapunov exponents for a selected two-dimensional system with stick–slip effect.