  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.
