A new family of 5D, 6D, 7D and 8D hyperchaotic systems from the 4D hyperchaotic Vaidyanathan system, the dynamic analysis of the 8D hyperchaotic system with six positive Lyapunov exponents and an application to secure communication design

Abstract

This work reports a new family of 5D, 6D, 7D and 8D hyperchaotic systems derived successively from the 4D hyperchaotic Vaidyanathan system (2018). The new 8D hyperchaotic system possesses six positive Lyapunov exponents. We discuss the dynamic properties of the new 8D hyperchaos system, describe its self-synchronisation and provide an application in secure communication. Anequivalent electronic circuit of the 8D hyperchaos is implemented using Multisim software to validate the physical feasibility of the system. As an application to secure communications, a new hyperchaotic transmission scheme is developed based on the drive-response synchronisation method and using all the 8D hyperchaos signals generated by the proposed system. With its six positive Lyapunov exponents, the proposed 8D hyperchaos system generates high complex behaviour. Thus, the new 8D hyperchaos system can be deployed in many engineering applications such as cryptosystems and secure communication.