Construction and Attractor Analysis of Discrete Chaotic Systems Based on Julia Fractal Transformation.

Fractals and chaotic systems play an important role in science and engineering. However, few scholars have focused on further deep integration of multiple fractals and multi-level cascaded chaotic systems to create new discrete chaotic maps. In this paper, we propose an innovative method to construct a series of new fractal chaotic maps by borrowing the concept of Julia fractal. Unlike previous fractal discrete map designs, this method enriches the dynamical behavior of the new maps by introducing the topological complexity of multiple fractal transformations into chaotic systems in terms of system structure. More importantly, it ensures that the new system dynamical structure satisfies the necessary condition for generating chaos through an internal feedback mechanism, i.e. the initial error is continuously transmitted in each state of the system iteration. The paper applies the method to eight types of discrete chaotic maps, generating various fractal chaotic maps, revealing new chaotic attractors as a result, and discussing the dynamical characteristics of discrete fractal chaotic maps through Lyapunov exponent, information entropy, spectral entropy, C0 complexity and bifurcation diagram analysis. The dynamical analysis indicates that the proposed fractal chaotic maps have higher complexity and stronger randomness. Consequently, the method proposed in this paper for generating new discrete chaotic maps through Julia fractal offers a novel approach to the design of chaotic systems, with promising potential for engineering and scientific applications. [ABSTRACT FROM AUTHOR]