Active control and electronic simulation of a novel fractional order chaotic jerk system

Abstract

The chaotic jerk system represents a class of nonlinear systems with unique, varied, and interesting characteristics and behavior. In this study, we proposed a modified fractional-order chaotic Jerk system by the introduction of two novel nonlinear terms and two constant terms. The nonlinear terms introduced are the exponential and tangential functions while the two parameters are a and b. Stability analysis of the fractional-order Jerk system was used to establish the parameter ranges for chaotic behavior in the system. Chaos in the system was confirmed via the Lyapunov exponents. The bifurcation diagram with respect to the parameters, a and b, as well as the fractional order, α were examined. The synchronization of the system was implemented using the active control method. Finally, the studied novel circuit was realized using MultiSIM electronic software for experimental validation.