中国物理B ›› 2026, Vol. 35 ›› Issue (7): 78702-078702.doi: 10.1088/1674-1056/ae0b3c

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Chaos and complexity in a cardiac pacemaker model with incommensurate fractional-order dynamics: Empirical validation and cardiovascular implications

Haneche Nabil1,† and Hamaizia Tayeb2   

  1. 1 Applied Mathematics and Modeling Laboratory, Department of Mathematics, Faculty of Exact Sciences, University of Mentouri Brothers, Constantine, Algeria;
    2 Mathematical Modeling and Simulation Laboratory, Department of Mathematics, Faculty of Exact Sciences, University of Mentouri Brothers, Constantine, Algeria
  • 收稿日期:2025-08-05 修回日期:2025-09-07 接受日期:2025-09-25 发布日期:2026-07-22
  • 通讯作者: Haneche Nabil E-mail:nabil.haneche@doc.umc.edu.dz

Chaos and complexity in a cardiac pacemaker model with incommensurate fractional-order dynamics: Empirical validation and cardiovascular implications

Haneche Nabil1,† and Hamaizia Tayeb2   

  1. 1 Applied Mathematics and Modeling Laboratory, Department of Mathematics, Faculty of Exact Sciences, University of Mentouri Brothers, Constantine, Algeria;
    2 Mathematical Modeling and Simulation Laboratory, Department of Mathematics, Faculty of Exact Sciences, University of Mentouri Brothers, Constantine, Algeria
  • Received:2025-08-05 Revised:2025-09-07 Accepted:2025-09-25 Published:2026-07-22
  • Contact: Haneche Nabil E-mail:nabil.haneche@doc.umc.edu.dz

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摘要： The dynamics of heart rhythms plays a pivotal role in physiological health, where chaotic behavior is often associated with pathological cardiac states. In this work, we investigate a fractional-order model of cardiac pacemaker dynamics using incommensurate derivatives to capture the complex memory effects and non-local interactions inherent in biological systems. We demonstrate that slight variations in the fractional orders induce rich dynamics, including chaos and coexisting attractors, signifying transitions between normal and dysfunctional rhythms. Crucially, our model exhibits wider chaotic regions than classical integer-order counterparts when the incommensurate derivatives are perturbed. Furthermore, we reveal pronounced multistability, where distinct chaotic attractors coexist under identical parameters, reflecting the system's capacity for abrupt transitions between physiological and pathological states. These findings advance the mechanistic understanding of rhythm disorders and highlight the critical role of fractional calculus in modeling cardiac dynamics.

关键词: cardiac pacemaker model, incommensurate fractional-order rhythm dynamics, chaos, bistability

Abstract: The dynamics of heart rhythms plays a pivotal role in physiological health, where chaotic behavior is often associated with pathological cardiac states. In this work, we investigate a fractional-order model of cardiac pacemaker dynamics using incommensurate derivatives to capture the complex memory effects and non-local interactions inherent in biological systems. We demonstrate that slight variations in the fractional orders induce rich dynamics, including chaos and coexisting attractors, signifying transitions between normal and dysfunctional rhythms. Crucially, our model exhibits wider chaotic regions than classical integer-order counterparts when the incommensurate derivatives are perturbed. Furthermore, we reveal pronounced multistability, where distinct chaotic attractors coexist under identical parameters, reflecting the system's capacity for abrupt transitions between physiological and pathological states. These findings advance the mechanistic understanding of rhythm disorders and highlight the critical role of fractional calculus in modeling cardiac dynamics.

Key words: cardiac pacemaker model, incommensurate fractional-order rhythm dynamics, chaos, bistability

中图分类号:  (Cardiac dynamics)

  • 87.19.Hh
05.45.-a (Nonlinear dynamics and chaos) 02.30.Hq (Ordinary differential equations) 05.45.Pq (Numerical simulations of chaotic systems)