A new 5D hyperjerk system: hyperchaos, Hopf bifurcation, synchronization, circuit design and an encryption application

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Abstract

Different from the classical triangular-structure hyperjerk forms, this work constructed a new five-dimensional (5D) hyperjerk system from a novel perspective and analyzed its dissipativity as well as the stability of the equilibrium point. By employing methods such as Lyapunov exponents, bifurcation diagrams, the 0-1 test, and Poincaré sections, the existence of a hyperchaotic attractor and the rich dynamical behaviors of the system were revealed. Based on normal form theory and symbolic computations, the existence of Hopf bifurcations and the stability of the bifurcation solutions were further investigated, and numerical examples were provided to validate the theoretical findings. By incorporating Lyapunov functions, we designed a suitable nonlinear controller that achieves global asymptotic synchronization of the hyperchaotic system. Simulation results demonstrated that the drive-response system achieves synchronization rapidly. In addition, an electronic circuit design scheme for the 5D hyperchaotic system was presented. The circuit simulation results were in good agreement with the numerical simulations, thereby verifying the physical realizability of the system. Finally, the practical application of the proposed hyperchaotic system in information encryption and decryption was explored. Based on this 5D hyperchaotic hyperjerk system, we developed encryption and decryption algorithms. From the analysis results of multiple metrics, including the correlation coefficient, information entropy, key space, number of pixel change rate, and unified average changing intensity, the proposed algorithm demonstrated favorable confidentiality and robust security performance.

Keywords

hyperchaotic hyperjerk system / Hopf bifurcation / hyperchaos synchronization / hyperchaotic circuit / hyperchaos encryption

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