An Exponential Jerk System: Circuit Realization, Fractional Order and Time Delayed Form with Dynamical Analysis and Its Engineering Application

Abstract

Simple dynamical systems are of interest always. In this paper, we propose a simple jerk system with one exponential nonlinearity. Dynamical properties of the proposed system are investigated. To show the practical realizability of the proposed system we implement the exponential jerk system using off the shelf components. Fractional order and time delays are considered as complex analysis patterns of nonlinear systems. We investigate the fractional order time delayed exponential jerk system. For numerical analysis we use the modified Adomian Decomposition Method. To show the engineering importance of the proposed system, we derive a pseudo random number generator based on it.Various test results are presented to show the randomness of the system.