A New 4D Hidden Hyperchaotic System with Higher Largest Lyapunov exponent and ‎its Synchronization

Abstract

Recently, the introducing high-dimensional systems with a larger Lyapunov exponent is very difficult and more complex. The paper introduces a new four-dimensional hyperchaotic system with a larger Lyapunov exponent compared with 15 works available in the literature. Th proposded system drive from the Lorenz-like system via a state feedback control approach  and cosis of teight trems only. This system lacks equilibrium points but can generate hidden attractors. Two positive Lyapunov exponents (LE) indicating hyperchaotic behavior are identified. The mathematical properties of this dissipative hyperchaotic system are both theoretically and numerically presented, encompassing Lyapunov exponents, Lyapunov dimension (Kaplan-Yorke dimension), Multistability, and Hybrid ‎projective synchronization (HPS). Various dynamic behavior are observed such as hyperchaotic, chaotic, chaotic 2-tours, and periodic behaviors. The paper provides proof of the main results through theoretical analysis and numerical simulations conducted in MATLAB V2021.