Finding Attractors of Continuous-Time Systems by Parameter Switching

TL;DR

This paper reviews a parameter switching algorithm that numerically approximates attractors in various classes of continuous-time dynamical systems, including continuous, discontinuous, integer, and fractional order systems.

Contribution

It systematizes existing results on the parameter switching algorithm and extends its application to multiple classes of dynamical systems with convergence analysis.

Findings

Algorithm effectively approximates attractors across system classes.

Convergence is analytically proven for continuous systems.

Numerical verification confirms applicability to discontinuous and fractional systems.

Abstract

The review presents a parameter switching algorithm and his applications which allows numerical approximation of any attractor of a class of continuous-time dynamical systems depending linearly on a real parameter. The considered classes of systems are modeled by a general initial value problem embedding dynamical systems which are continuous and discontinuous with respect to the state variable, and of integer and fractional order. The numerous results, presented in several papers, are systematized here on four representative known examples representing the four classes. The analytical proof of the algorithm convergence for the systems belonging to the continuous class is briefly presented, while for the other categories of systems the convergence is numerically verified via computational tools. The utilized numerical tools necessary to apply the algorithm are contained in five appendices.