Fractional memory and spatially varying conduction in spiral-wave dynamics of excitable media

This is the authors' abstract. We don't add key points for this paper.

This work develops a fractional framework for spiral-wave dynamics in excitable media by combining temporal memory with anomalous spatial conduction through a fractional complex Ginzburg–Landau-type model. Temporal memory is introduced through the Caputo derivative, while a fractional spatial operator represents nonlocal and geometry-dependent transport. Both constant and spatially varying fractional orders describe homogeneous and heterogeneous conduction environments, with the latter representing fibrosis-like spatial profiles. Numerical simulations demonstrate the emergence, drift, fragmentation, and suppression of spiral waves as temporal and spatial parameters vary. Decreasing the temporal order strengthens hereditary effects and modifies recovery dynamics, whereas decreasing the spatial order enhances nonlocal transport and redistributes excitation across spatial scales. Spatially heterogeneous fractional profiles generate conduction imbalance and destabilization, producing transitions between coherent rotation, fragmented activity, and suppressed states. Energy, thermodynamic entropy, and Fourier analyses characterize changes in gradient energy, dynamical disorder, and excitation modes associated with these transitions. Results establish a mathematical framework for examining how fractional memory and anomalous heterogeneous transport influence spiral-wave organization in excitable media. Although motivated by electrophysiological phenomena, the formulation is a reduced phenomenological model rather than a detailed ionic cardiac model and therefore identifies general mechanisms rather than direct quantitative predictions of cardiac action potentials.