A more chaotic and easily hardware implementable new 3-D chaotic system in comparison with 50 reported systems

Abstract

This paper attempts to construct a new 3-D chaotic system which is easily hardware realisable and fulfil the requirement of a real-life application. The proposed system is relatively more chaotic (based on the first Lyapunov exponent) and has larger bandwidth than 50 available chaotic systems. Lyapunov spectrum and bifurcation diagram of the system reveal that it has chaotic behaviour for a wider range of its parameters. Such characteristic is helpful for an easy hardware realisation of the system. It is to be noted that the reported systems with hidden attractors are not considered here for the comparison. The proposed system has more complexity and disorder due to several unique properties like asymmetry to principle coordinates, dissimilar and asymmetrical equilibria, and non-uniform contraction and expansion of volume in phase space. The proposed system also exhibits asymmetric pairs of coexisting attractors during its operation in two modes. The new system has different routes to chaos including crisis, an inverse crisis, period-doubling and reverse period-doubling routes to chaos with the variation of parameters. MATLAB simulation results confirm the claims, and the results of hardware circuit realisation validate the simulation results. An application of the new system is shown by masking and retrieving an information signal. It is also shown that the proposed system is better than a well-known Lorenz chaotic system for this application. A system with the above unique properties is rare in the literature.