Stability and chaos with mathematical control of 4-D dynamical system

Abstract

A new four-dimensional continuous-time system is dealt in this paper. The system employs eight simple terms involving two quadratic cross-product nonlinear terms. The fundamental characteristics of the system are analyzed by means of equilibrium points, stability analysis, dissipativity, wave form analysis, Lapiynuov Exponents and Kaplan-Yorke dimension. The maximum value of Lapiynuov exponent is obtain as (1.660748) andKaplan Yorke dimension obtain as (), that show the system is unstable and highly chaotic. As well, an optimal controller by adaptive control strategy is established to be system trajectories are stable. Finally, Adaptive synchronization of system (1) is clarified. Tables are made to compare the theoretical and graphical results of the system before and after control.