Hybrid Chaotic Systems Via Piecewise Setting: Theory, Methods, and Applications

ABSTRACT This study delves into the concept of hybrid chaos, which fuses elements of chaos and order to create dynamic, adaptable systems. Chaos, often marked by unpredictable behavior, fosters creativity and innovation. Hybrid chaos, however, seeks to integrate both chaotic and ordered components to form resilient systems. Across various fields—such as creativity, biology, and technology—hybrid chaos opens up new possibilities by merging structured systems with random, chaotic elements. Moreover, the incorporation of stochastic processes further enhances the system's adaptability and complexity. This paper aims to develop novel hybrid chaotic systems by combining different chaotic systems over varying intervals, advancing our understanding of hybrid chaos and its potential applications in real‐world scenarios.