A New Nine-Dimensional Dynamical Chaotic System: Construction, Chaotic Behavior, and Stability Analysis Based on Routh-Hurwitz Criterion

Abstract

Although chaos frequently occurs in nonlinear systems; this is not always the case. Consequently, a great deal of research has been done to determine whether systems, given particular initial conditions or characteristics, are capable of exhibiting chaos. Some systems are exceptionally complex due to their high dimensionality and simple nonlinear terms or parameter values. Thus, the development of higher-dimensional chaotic systems has become an important area of study in chaos theory due to its more complex chaotic features. This paper presents and analyzes a hyper chaotic system built with nonlinear equations in nine dimensions. Fifteen positive factors were employed to create a hyper chaotic system in nine dimensions. Mathematica simulation is used to examine the wave form analysis, Lyapunov proponent, sensitivity reliant on on early condition (SDIC) analysis, chaotic behavior, fractal dimension (), and bifurcation of the proposed system. According to a well recognized definition, a system is considered chaotic if its Lyapunov exponent is positive or if it satisfies SDIC on its domain. And Investigation the Routh-Hurwitz criterion used to examine its stability behavior. Over time, the separation from the initial state will likewise increase. It was understood that even a slight alteration to the initial values would cause the chaotic behavior to become extremely sensitive. Three positive Lyapunov exponents and a non-cyclical time-domain waveform demonstrating more complicated dynamical features highlight the hyper-chaotic nature of the proposed system. In the system, every fixed point is unstable