Another new chaotic system: bifurcation and chaos control

TL;DR

This paper introduces a new three-dimensional chaotic system, analyzes its bifurcation behavior, and demonstrates chaos control by adjusting a time-scale parameter, contributing to the understanding of chaos dynamics.

Contribution

The paper presents a novel 3D autonomous system with bifurcation analysis and chaos control via time-scale ratio adjustment, which is a new approach in chaotic system modeling.

Findings

System exhibits Hopf bifurcation and period-doubling route to chaos.

Analytical derivation of Lyapunov coefficient characterizes bifurcation nature.

Chaos is controllable by tuning the time-scale ratio parameter.

Abstract

We propose a new simple three-dimensional continuous autonomous model with two nonlinear terms and observe the dynamical behavior with respect to system parameters. This system changes the stability of fixed point via Hopf bifurcation and then undergoes a cascade of a period-doubling route to chaos. We analytically derive the first Lyapunov coefficient to investigate the nature of Hopf bifurcation and also investigate well-separated regions for different kinds of attractors in two-dimensional parameter space. Next, we introduce a time-scale ratio parameter and calculate the slow manifold using geometric singular perturbation theory. Finally, the chaotic state is annihilated by decreasing the value of the time-scale ratio parameter.