Nonlinear dynamics and chaos in fractional-order cardiac action potential duration mapping model with fixed memory length

In this paper, a novel one-dimensional mapping model for cardiac action potential duration (APD) is proposed, introducing the concept of ``fixed memory length'' within a fractional-order discrete framework. Unlike traditional fractional models with infinite memory or short-memory maps, this approach explicitly incorporates a controlled memory span, allowing a more realistic representation of cardiac tissue dynamics. The model reveals new nonlinear behaviors influenced by memory effects, analyzed through bifurcation diagrams and validated using the 0-1 test for chaos under varying pacing periods (ts). The results demonstrate that fixed memory length plays a fundamental role in dynamic instability, leading to alternans and chaotic behaviors. Clinically, this modeling provides deeper insight into the mechanisms underlying cardiac arrhythmias and irregular rhythms, offering potential applications to improve arrhythmia prediction and guide therapeutic pacing strategies.