Exploring the Duffing Equation: Numerical Analysis, Discrete Dynamics,and Ecological Modeling

This research paper delves into the dynamics of a novel ecology model that describes the intricate interplay between radioactivity and cancer cases. Organized into three main sections, the study covers numerical analysis using advanced techniques, the analysis of discrete dynamical systems, and explores the potential applications of the model in the context of cancer research and ecological systems. By conducting a comprehensive bifurcation analysis, we unveil the model's sensitivity to external factors, interactive behaviors between radioactivity and cancer cases, and the emergence of multiple attractors. These findings open up new avenues for understanding cancer dynamics, ecological systems, and clinical scenarios, where even subtle variations in external factors can lead to significant variations in cancer incidence. The insights gained from this study have promising implications for both theoretical and applied research in cancer epidemiology and ecology, providing a deeper understanding of the complex dynamics underlying these systems. In our research, we present a new ecology model that reveals the intricate and often nonlinear relationship between radioactivity and cancer incidence, offering novel insights into cancer dynamics and environmental influences.