Nonlinear Phenomena in Complex Systems, 2026, Vol.29, No.3, pp.232

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2026, Vol.29, No.3, pp.232 - 245

Influence of Time Lag on Cardiac Excitation Using the Aliev-Panfilov Model

Kalyan Das, A. Sabarmathi, V. S. V. Naga Soundarya Lakshmi, and Ramakrishna Mundugar

The Aliev-Panfilov model is a widely adopted mathematical representation of cardiac excitation, renowned for capturing the essential restitution properties of cardiac tissue. In this study, we extend the classical model by incorporating a physiologically motivated temporal delay to account for latency in cellular signaling and tissue-level propagation. We begin by establishing the well-posedness of the delay model, proving the existence, uniqueness, and boundedness of its solutions. A detailed equilibrium analysis is conducted to determine conditions for the existence and stability of steady states, revealing how time delay alters the system's dynamical behavior. To assess global stability, we construct suitable Lyapunov functions, while local stability of the non-delayed system is examined using the Routh--Hurwitz criterion. The delay-augmented model is further analyzed through its characteristic equation, leading to a bifurcation study that identifies Hopf bifurcations ``marking the emergence of sustained oscillations'' as the delay parameter crosses critical thresholds. Our results demonstrate that even small delays can destabilize the system, potentially inducing abnormal rhythmic patterns analogous to cardiac arrhythmias. This work underscores the significant role of temporal delay in cardiac dynamics and provides a rigorous mathematical framework for understanding delay-induced excitability changes in cardiac tissue.

Key words: Aliev-Panfilov Model, Cardiac Excitation

DOI: https://doi.org/10.5281/zenodo.23278040

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