A New Nine-Dimensional Dynamical Chaotic System: Construction and Synchronized of Hyper-Chaotic System with Active Control with Circuit Realization

Abstract

Very often bedlam occurs in a nonlinear model; however, it is not always the case. This has led to extensive research into identifying which systems can display chaos under specific initial conditions or attributes. Due to their enormous dimensionality and straightforward nonlinear terms or parameter values, certain systems are particularly difficult. Thus, higher-dimensional chaotic systems' more intricate chaotic characteristics have made their development a crucial field of study in chaos theory. This work describes and examines a 9-D hyper-chaotic model constructed with nonlinear equations. A 9-D were used to generate a hyper-chaotic model with fifteen positive coefficients. The proposed model's The dependence on the initial state, which depends on the sensitivity of the proposed model and its Wave analysis, and Lyapunov exponents have chaotic behavior, fractal dimension and bifurcation are all examined using Mathematica simulation. A widely accepted definition of chaos states that a model, if has a positive Lyapunov exponent or satisfies in its domain, it is chaotic. The distance between the original conditions will also grow with time. It was recognized that the chaotic behavior would become exceedingly sensitive to even a small change in the starting values. More complex dynamical behaviors were demonstrated using a non-cyclical time-domain waveform with three positive Lyapunov exponents and Active Control Matching Synchronization in Hybrid Results for the new model(9-D), the hybrid synchronization is identical to the hyper-chaos and nature of the stated model is demonstrated by active control and circuit realization of hyper-chaotic model.