Bifurcation of Novel Seven-Dimension Hyper Chaotic System

Abstract

Abstract In this paper, introduced a novel seven dimensions (7D) nonlinear hyperchaotic system in third-order. A chaotic behavior that has twelve positive parameters for novel 7D hyperchaotic is analyzed through calculating the Lyapunov exponent, attracter of the system, fractional dimension, influence parameters, dissipative, bifurcation path, and phase portraits. It is well known that one of the chaotic definitions is the novel 7D chaotic if it satisfies positive Lyapunov exponent at each point on its domain (eventually periodic). The results from the numerical analysis of Lyapunov exponents, bifurcation have shown that there are periodic dynamic behaviors, quasi-periodic, the existence of chaotic attractors, and hyperchaotic for our analyzed to the proposed system. Also, some complex dynamic behaviors are discussed, such as equilibrium stability, Besides, discuss when a parameter changes a properties phase portrait change also. The dynamics of the proposed novel 7D hyperchaotic simulated and implemented using the Mathematica program provided qualitatively and it illustrated phase portraits.