Design and Analysis of a Novel Six-Dimensional Hyper Chaotic System

Abstract

The chaotic system has been widely studied. A new six-dimension hyper chaotic system is introduced in this paper. We used a new chaotic system based on a six-dimension for the purpose of increasing chaos in the system, where the new system has eleven positive parameters, complicated chaotic dynamics behaviors and gives an analysis of the new systems. The basic characteristics and dynamic behavior of this system are investigated with a presence of chaotic attractor, Dissipativity, symmetry, equilibrium points, Lyapunov Exponents, Kaplan-Yorke dimension, waveform analysis and sensitivity toward initial conditions. The results of the analysis exhibit that the new system contains three unstable equilibrium points and the six Lyapunov exponents. Maxim non-negative Lyapunov Exponent (MLE) is obtained as 4.72625, and Kaplan-Yorke are obtained as 3.92566, and the new system characteristics with, unstable, high complexity, and unpredictability, the new system dynamics is simulated utilizing MATHEMATICA program. The phase portraits and the qualitative properties of the new hyper chaotic system have been described at the detail.