Design and Analysis of a New Four-Dimensional Chaotic System : Study of Dynamical Properties and Chaos Verification

Abstract

Presented a new (4D) four-dimensional hyperchaotic system with four nonlinear terms and thirteen positive parameters. The chaotic system is tested through Mathematica was used to confirm the results and prove that the system is super chaotic the complex dynamics of the new system and its basic characteristics for instance Equilibrium Point, attractors, waveform analysis, Lyapunov exponents, sensitive dependent to initial conditions (SDIC) and fractal dimension to prove the chaotic behavior of the system. A change in the initial values leads to a significant change in the chaotic system, which is vulnerable to any change that occurs. As a result of the four equations generated, two fixed points were obtained: F0, F1. These points prove the chaotic nature of the system. Also, two nonnegative Lyapunov values were obtained, which rely on these values to identify the system's sensitivity to the values between the close points. The values were used to generate phase images to prove the randomness of the system. Also, the sensitivity of the key was tested, and it was found to be large enough to resist attackers.