A new family of 9D and 10D hyperchaotic systems from the 8D hyperchaotic Benkouider system, the bifurcation analysis of the 10D hyperchaotic system, circuit design and an application to secure voice communication

Abstract

This work presents a new 10D polynomial hyperchaotic system with eight positive Lyapunov exponents. We propose a family of new 9D and 10D hyperchaotic systems, which are derived from the 8D hyperchaotic Benkouider system (2020). With its eight positive Lyapunov exponents, the proposed 10D hyperchaotic system generates a very complex behaviour than the existing systems, which makes it very useful in many fields of applications, especially in secure communication. Major properties of the new system are investigated using Lyapunov exponents, bifurcation diagrams, phase portraits, equilibrium points, Kaplan-Yorke dimension and multistability. In addition, an equivalent electronic circuit is implemented using Multisim software to validate the physical feasibility of the constructed 10D hyperchaotic system. Finally, a new secure voice communication scheme is developed based on the chaotic masking approach and using all the complex hyperchaotic signals generated by the new 10D hyperchaotic system.