Hopf Bifurcation, Periodic Solutions, and Control of a New 4D Hyperchaotic System

Yu Liu, Yan Zhou () and Biyao Guo
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Yu Liu: College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, China
Yan Zhou: College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, China
Biyao Guo: College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, China

Mathematics, 2023, vol. 11, issue 12, 1-14

Abstract: In this paper, a new four-dimensional (4D) hyperchaotic biplane system is designed and presented. The dynamical properties of this new system are studied by means of tools such as bifurcation diagrams, Lyapunov exponents and phase diagrams. The Hopf bifurcation and periodic solutions of this hyperchaotic system are solved analytically. In addition, a new hyperchaotic control strategy is applied, and a comparative analysis of the controlled system is performed.

Keywords: hyperchaotic system; Hopf bifurcation; periodic solutions; hyperchaos control; normal form theory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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