Another New Chaotic System: Bifurcation and Chaos Control

Article Type

Research Article

Publication Title

International Journal of Bifurcation and Chaos

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 period-doubling route to chaos. We analytically derive the first Lyapunov coefficient to investigate the nature of Hopf bifurcation. We investigate well-separated regions for different kinds of attractors in the two-dimensional parameter space. Next, we introduce a timescale ratio parameter and calculate the slow manifold using geometric singular perturbation theory. Finally, the chaotic state annihilates by decreasing the value of the timescale ratio parameter.

DOI

10.1142/S0218127420501618

Publication Date

9-15-2020

Comments

Open Access, Green

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