Multistability in Piecewise Linear Systems by Means of the Eigenspectra Variation and the Round Function

TL;DR

This paper introduces a multistable piecewise linear system controlled by a round function, demonstrating how eigenspectra variation influences system stability and attractor configurations through bifurcation analysis.

Contribution

It presents a novel PWL system using the round function for switching, enabling control over multistability and attractor states via eigenspectra manipulation.

Findings

System exhibits multistability with multiple attractors.

Eigenvalue adjustments induce bifurcations leading to different stability states.

Numerical analysis confirms control over attractor configurations.

Abstract

A multistable system generated by a Piecewise Linear (PWL) system based on the jerky equation is presented. The systems behaviour is characterised by means of the Nearest Integer or round(x) function to control the switching events and to locate the corresponding equilibria among each of the commutation surfaces. These surfaces are generated by means of the switching function dividing the space in regions equally distributed along one axis. The trajectory of this type of system is governed by the eigenspectra of the coefficient matrix which can be adjusted by means of a bifurcation parameter. The behaviour of the system can change from multi-scroll attractors into a mono-stable state to the coexistence of several single-scroll attractors into a multi-stable state. Numerical results of the dynamics and bifurcation analyses of their parameters are displayed to depict the multi-stable states.