Dynamic complexity of fifth-dimensional Henon map with Lyapunov exponent, permutation entropy, bifurcation patterns and chaos

Abstract

The research analyses how the classic Henon map's adjustments affected the system's dynamical behavior and bifurcation frameworks. Analyzing the updated Henon map's parameter space reveals intricate patterns and transitions as the system bifurcates. The dynamical evolution of the map is studied through numerical simulations, providing insights into the emergence of novel features and behaviors. Furthermore, the Lyapunov exponent of the fifth-dimensional Henon map is calculated to quantify the system's sensitivity to initial conditions. The Lyapunov exponent serves as a crucial indicator of chaos and stability, aiding in the characterization of the map's complex dynamics. The paper presents dissipative, permutation entropy, basin of attraction and a comprehensive examination of the Lyapunov exponent across parameter ranges, shedding light on the system's overall stability and chaos. A number of theorems and a study on stability are demonstrated in this article. The results highlight the profound impact of modifications on the Henon map's dynamics, offering a deeper understanding of its behavior and bifurcation scenarios. This research adds to the larger body of knowledge in the areas of unusual systems and how they act in the context of the chaos hypothesis on the behavior of the Henon map. The results show that parameter adjustments substantially shape the dynamical complexity of the Henon map. This study presents a fifth-dimensional Hénon map-based encryption and random bit generator for secure image cryptography.