Changing Dynamics of the First, Second and Third Approximations of the Exponential Chaotic System and Their Application in Secure Communication Using Synchronization

In this manuscript a chaotic system with exponential term has been considered and studied. Its basic dynamical properties such as time series, phase plots, Lyapunov exponents, bifurcation diagrams, equilibrium points, Poincare section etc. have been discussed and compared with its first, second and third approximate systems. The main aim of this study is to explore the dynamics of the approximations of the exponential chaotic systems. Also, the controllers have been designed to synchronize the chaotic system and its approximations using a technique "compound combination synchronization" and show its application in the field of secure communication. Simulations have been provided to show the efficacy of the used method.