Track: Modeling and Simulation

Abstract

Chaotic systems deal with nonlinear dynamical systems which are highly sensitive to changes in the initial conditions. This paper reports the finding of a new 3-D chaotic system with three nonlinearities – two quadratic nonlinearities and a quartic nonlinearity. The phase plots and dynamic analysis of the new chaotic system are described by means of MATLAB plots, bifurcation diagram, Lyapunov exponents, etc. The hyperchaotic system has a unique saddle-point equilibrium at the origin. As a control application, the adaptive synchronization of the new chaotic system with itself is obtained using Lyapunov stability theory. Finally, an electronic circuit of the new chaotic system with MultiSIM is designed and a good match between the plots of the theoretical chaotic model and the circuit model is obtained. The electronic circuit model validates the new theoretical chaotic model developed in this work.