Systematic construction of high dimensional fractional-order hyperchaotic systems

Abstract

Abstract The problem of designing fractional-order hyperchaotic systems (FOHSs) by a consistent and systematic procedure is still an open one at large. The tedious hit and trial design procedures adopted in literature to generate hyperchaos pose as a hindrance; especially when the dimension of the system is high. The paper thus presents a solution to the above problem and further discusses the application of FOHSs by putting forward three proposals. First is the design of the simplest possible single state nonlinear feedback controller based on fractional-order stability theorems for creating hyperchaos from a nominal system. The design is organised and even higher dimensional FOHSs can be easily constructed. Secondly, a hybrid synchronisation controller is designed so that the FOHSs obtained using the proposed systematic methodology, are both completely synchronised and antisynchronised simultaneously. Thirdly, a public key cryptographic algorithm is presented using the higher unpredictable nature and complexity of FOHSs to encrypt and decrypt private messages. Two representative examples presented in this work distinctly confirm the effectiveness of the proposed techniques.