Chaos suppression in a Gompertz-like discrete system of fractional order

TL;DR

This paper introduces a fractional-order Gompertz-like discrete system and demonstrates chaos suppression using impulsive control, validated through numerical methods including Lyapunov exponents and the 0-1 test.

Contribution

It presents the first fractional-order variant of a Gompertz-like discrete system and applies impulsive control to suppress chaos within this framework.

Findings

Chaos can be effectively suppressed in the fractional-order system.

Numerical methods confirm the stability of the controlled system.

Lyapunov exponents and 0-1 test validate chaos suppression.

Abstract

In this paper we introduce the fractional-order variant of a Gompertz-like discrete system. The chaotic behavior is suppressed with an impulsive control algorithm. The numerical integration and the Lyapunov exponent are obtained by means of the discrete fractional calculus. To verify numerically the obtained results, beside the Lyapunov exponent, the tools offered by the 0-1 test are used.