A systematic methodology for constructing hyperchaotic systems with multiple positive lyapunov exponents and circuit implementation

This paper aims at developing a systematic methodology for constructing continuous-time autonomous hyperchaotic systems with multiple positive Lyapunov exponents. To overcome the essential difficulty in balancing between local instability and global convergence, this paper initiates a new methodology for designing a dissipative hyperchaotic system with a desired number of positive Lyapunov exponents. A general design principle and the corresponding implementation steps are then developed. Three representative examples are shown to validate the proposed principle and implementation scheme. Moreover, a hyperchaotic circuit is constructed to verify a 6-dimensional hyperchaotic system with four positive Lyapunov exponents. Comparing with the traditional trial-and-error approach, the proposed method can design various hyperchaotic systems with any desired number of positive Lyapunov exponents in a systematic way.