Dynamics of q-deformation discrete fractional chaotic Lorenz system: Exploring chaos, stabilization, and synchronization

Abstract

The dynamical system has a wide range of applications in different fields of science, such as mathematics, banking, ecology, economy, meteorology, etc. The main objective of this research is to analyze the dynam ics of q-deformation fractional chaotic systems and their stability and synchronization. The motivation behind this research is the tremendous appetite for improving the previous knowledge. This research has contributed significantly to the field of dynamical systems. The thesis includes three chapters, each centered mainly on the different concepts related to the dynamical system. The first chapter introduces a dynamical system, covering some basic concepts, including well-known theorems such as the attracting fixed-point theorem, repelling fixed-point theorem, and some basic results from discrete fractional calculus. This chapter provides a strong basis for the next two chapters. The sources of the basic knowledge are provided by following [1, 2, 3, 4, 16]. In the second chapter, we reviewed literature about q-deformation discrete fractional chaotic maps [5]. In this chapter, we investigate the dynamics by incorporating the q-deformation operator into the discrete Henon map. This thorough analysis involves a comprehensive examination of the Henon map dynamics under q-deformation, revealing the complexities of chaos, stabilization, and synchronization within this modified framework. Ultimately, the dynamical analysis of the q-deformed Henon map is validated through numerical simulations [5, 6]. The third chapter reveals the development of the concepts based on previous knowledge. Within the confines of the third chapter, we undertake an exploration into the realm of chaos, synchronization, and stabilization within the discrete q-deformed fractional Lorenz system. This section serves as a focused investigation, unraveling the intricacies of dynamic behavior in the modified system [7, 8, 9]