Analysis, Synchronization, Circuit Implementation, and Encryption Application of a New 5D Hyperchaotic Hyperjerk System

ABSTRACT

This paper proposes a novel 5D hyperchaotic hyperjerk system with a non‐triangular structure. The equivalence between the proposed system and the classical hyperjerk systems is clarified, the dissipativity of the system is verified, and the existence of an equilibrium curve is proved. For a typical set of system parameters, the Lyapunov exponents are calculated as , corresponding to a Kaplan–Yorke dimension of 4.064, which confirms the hyperchaotic behavior of the system. Subsequently, by employing Lyapunov exponents, bifurcation diagrams, Poincaré mapping, the 0‐1 test, and power spectra, rich dynamical characteristics are revealed, including hyperchaos, chaos, coexisting hyperchaotic attractors, and quasi‐periodicity. A nonlinear controller based on a Lyapunov function is designed to achieve global asymptotic synchronization of the hyperchaotic system. Simulation results confirm that the drive‐response system achieves rapid synchronization. In terms of hardware implementation, an analog circuit of the 5D hyperchaotic system is constructed using 38 resistors, 13 operational amplifiers, and other electronic components. The close agreement between circuit simulations and numerical simulations verifies the physical realizability of this 5D hyperchaotic hyperjerk system. Furthermore, the proposed system can be applied to the field of information security. Based on this system, an image encryption and decryption algorithm is designed. Example simulations demonstrate the effectiveness and high security of the proposed algorithm.