A Note on Chaos of a Modified Piecewise Linear Discontinuous System with Multiple-Well Potentials: Melnikov Approach with Simulations

The topic of chaotic thresholds for piecewise linear discontinuous (PWLD) systems with multiple-well potentials is a persistent topic in the research of a number of authors. In this article we investigate the chaos of a modified piecewise linear discontinuous (MPWLD) system. The model, containing N free parameters, could be of interest to specialists working in this area. With a specially developed software product, we generate the Melnikov equation M(t)=0 and examine all its zeros. This opens up an opportunity for researchers to correctly understand and formulate the classical Melnikov criterion for the possible occurrence of chaos in dynamical systems. Several simulations are composed. We also demonstrate some specialized modules for investigating the dynamics of the proposed model. Intriguing and new generalizations made through probabilistic constructions are considered.