A New 4-D Conservative System with Hyperchaos and Two Saddle-Focus Hyperbolic Equilibria Points

As advancements in applied sciences and technology continue, various dissipative nonlinear systems have emerged. However, the conservative systems have received little attention in previous research. The purpose of this paper is to introduce a novel four-dimensional conservative system with hyperchaotic behavior. This system is derived from the Lorenz -like system through the use of a state feedback control strategy. The resulting system features two saddle -focus hyperbolic equilibria. Various dynamical characteristics are examined theoretically and numerically, including its equilibria, Jacobian matrix, Lyapunov exponents, Lyapunov dimension (Kaplan -Yorke dimension), Multistability, and Complete Synchronization. Additionally, numerical simulation using MATLAB 2021 confirms the theoretical results. (c) 2024 L&H Scientific Publishing, LLC. All rights reserved.