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

Abstract The dynamics of heart rhythms play a pivotal role in physiological health, where chaotic behavior is often linked to pathological cardiac states. In this work, we investigate a fractional-order model of cardiac pacemaker dynamics using incommensurate derivatives to capture complex memory effects and non-local interactions inherent in biological systems. We demonstrate that slight variations in these 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 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 cardiac dynamics modeling.