Bifurcation Analysis and Chaotic Behavior of the Concatenation Model with Power-Law Nonlinearity

Abstract

This paper presents a comprehensive analysis of the concatenation model with power-law nonlinearity. The research encompasses multiple key aspects, providing a detailed exploration of the model's behavior and implications within the context of nonlinear dynamics and optics. The study commences with an in-depth bifurcation analysis, aiming to unravel the intricate dynamics and transitions within the system. This analysis not only uncovers the system's behavior under varying conditions but also sheds light on its stability and the emergence of bifurcation phenomena. Our research delves into the retrieval of soliton solutions within the model. The exploration of solitons is of paramount significance, offering insights into localized, self-sustaining waveforms that often play a crucial role in nonlinear systems. These soliton solutions are identified, characterized, and their relevance to the model is established. The paper addresses the complex dynamics of the system in the presence of perturbation terms. By incorporating perturbations into the analysis, we elucidate how external influences impact the system's behavior and lead to chaotic phenomena. This analysis helps uncover the system's sensitivity to external factors and provides a deeper understanding of chaotic behavior.