Bifurcations of the GKdV–mKdV-Like System with Medical Applications

Employing bifurcation theory in dynamical systems, we delve into analyzing the nonlinear wave dynamics and asymptotic behaviors of the generalized KdV–mKdV-like system. Our exhaustive analysis across varied parameter regimes uncovers a wide range of wave phenomena tied intricately to the system parameters. Our work elucidates the stability and complex dynamics in related biological systems, paving a transformative way for medical applications. The intricate dynamics revealed by the bifurcation phenomena in the GKdV–mKdV-like system are promising for advancing medical research and clinical practice, particularly through AI-driven optimization. This interdisciplinary approach bridges mathematical theory and medical innovation, opening a door for predictive modeling of health conditions and proactive healthcare strategies.