A Chaotic System with Infinite Number of Equilibria Located on an Exponential Curve and Its Chaos-Based Engineering Application

Abstract

This paper proposes a novel chaotic system with infinite number of equilibria located on an exponential curve. It signifies an exciting category of dynamical systems which display many features of regular and chaotic motions. The proposed chaotic system belongs to the general category of chaotic systems with hidden attractors. Moreover, some theoretical analyses of the chaotic system's dynamical characteristics are presented. Using the developed chaotic system, the new random number generator and encryption algorithm have been designed. Encryption application and security analysis are presented verifying its feasibility.