Abstract
In this work, analytic and designed a new self -existed 5-D with thirteen terms nine of the term exhibit linearity, while the remaining one demonstrates nonlinearity. It has the highest Lyapunov Exponent with three positive ones to leverage the sequence in data security, encryption, and other related aspects, it’s advantageous to utilize a complex system where the key remains unbreakable It contains fifteen keys sensitive ICs and parameters. The system is a highly intricate dynamical system characterized by two equilibrium points, as demonstrated through examinations such as observation of phase plane trajectories, the investigation into eigenvalue structure, and assessment of dissipative stability. These analyses provide evidence supporting the existence of chaotic and hyperchaotic attractors within the system. The results of the simulations are derived from MATLAB 2021b, and Mathematica 11. A detailed and comprehensive evaluation of the recommended techniques has been carried out, offering insights into their effectiveness and suitability for theoretical computation and numerical simulation.
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