Constructing some discrete 4-D hyperchaotic systems

Abstract

Modeling real life phenomena often leads to complex nonlinear dynamics such as bifurcation and chaos. The study of such problems has attracted interest of many scientists over the past decades. In this paper, we present a method for constructing some discrete four dimensional (4-D) hyperchaotic systems. A nonclassical procedure for discretising autonomous 4-D continuous hyperchaotic systems is applied; a parameter is introduced in this process. By adjusting this parameter, until we obtain exactly two equal-positive Lyapunov exponents, a new discrete 4-D hyperchaotic system is realised. We prove that these discrete systems are bounded-input bounded-output (BIBO) stable. Our illustrative results show that the constructed discrete systems and their continuous counterparts have similar phase portraits.