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

Guanghua Wei; Xiaorong Zhang; Zhoujin Cui; Guanghua Wei; Xiaorong Zhang; Zhoujin Cui

doi:10.3934/math.2025672

AIMS Mathematics

2025, Volume 10, Issue 6: 14996-15011. doi: 10.3934/math.2025672

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

1.
School of Science, Jinling Institute of Technology, Nanjing, 211169, China
2.
School of Economics and Management, Jiangsu Maritime Institute, Nanjing, 211170, China
3.
School of Mathematical Sciences, Jiangsu Second Normal University, Nanjing, 210013, China

Received: 19 April 2025 Revised: 14 June 2025 Accepted: 24 June 2025 Published: 30 June 2025
MSC : 34A08, 34K37, 37N99

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.
- fractional-order coronary artery model,
- primary resonance,
- averaging method,
- amplitude-frequency equation
Citation: Guanghua Wei, Xiaorong Zhang, Zhoujin Cui. Primary resonance analysis of a novel fractional-order coronary artery model[J]. AIMS Mathematics, 2025, 10(6): 14996-15011. doi: 10.3934/math.2025672

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Abstract

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.

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