Primary resonance analysis of a novel fractional-order coronary artery model

This paper analyzed the primary resonance of a novel fractional-order coronary artery model, exploring cardiovascular diseases related to vascular behavior from the nonlinear dynamics perspective. By applying the averaging method, approximate analytical solutions and the amplitude-frequency equation were derived, whereas Lyapunov stability theory was utilized to analyze the steady-state behavior. Numerical simulations validated the accuracy of the analytical approach, demonstrating close agreement between theoretical predictions and computational results. Key findings include the identification of parameter-driven bifurcations that modulate resonance amplitude and stability. Specifically, a lower fractional order $q$ and reduced damping $\mu$ amplify resonant responses, while increased pulse pressure $F$ correlates with elevated spasm risk. These results provide a theoretical framework for understanding how blood vessel viscoelasticity and external stimuli influence cardiovascular dynamics, offering insights for developing diagnostic tools and therapeutic strategies to mitigate coronary artery spasm and related cardiovascular diseases.