Transition from stable orbit to chaotic dynamics in hybrid systems of Filippov type with digital sampling

TL;DR

This paper investigates how digital sampling affects the dynamics of hybrid Filippov systems, revealing a transition from stable to chaotic behavior and establishing a scaling law relating sampling time to attractor size.

Contribution

It introduces a detailed analysis of the transition from stable limit cycles to chaos in hybrid systems under digital sampling, including numerical and analytical insights.

Findings

Scaling law proportional to sampling time for small τ

Transition to nonlinear scaling for large τ

Change in attractor boundedness explains the phenomenon

Abstract

We demonstrate on a representative example of a planar hybrid system with digital sampling a sudden transition from a stable limit cycle to the onset of chaotic dynamics. We show that the scaling law in the size of the attractor is proportional to the digital sampling time $\tau$ for sufficiently small values of $\tau.$ Numerical and analytical results are given. The scaling law changes to a nonlinear law for large values of the sampling time $\tau.$ This phenomenon is explained by the change in the boundedness of the attractor.