Spatiotemporal dynamics in the bi-layer memristive Morris-Lecar neurons with different obstacles

Chaos. 2026. Vol. 36. No. 10. P. 1–13.

Seralan V., Srinivasan S., Anitha K., Karthikeyan R., Popov V.

We report spiral-wave transitions in the memristive Morris-Lecar neuron model with differently structured obstacles
in single and bilayer configurations. Wave propagation is initiated by applying an external periodic stimulus to the
left-side nodes of the excitable media. During interactions with obstacles, rich spiral patterns emerge in both single-layer and bilayer configurations across various amplitudes and frequencies of the external stimulus, as well as for different diffusion coefficients. The spatio-energy is also calculated to demonstrate the existence of a spiral core within stable spiral waves. The statistical synchronization factor is computed over a range of diffusion coefficients to assess the presence of spiral waves and the absence of instabilities. Building on these single-layer dynamics, we then investigate multilayer effects by extending our study to a bilayer system, with one layer containing obstacles. We observe the transition of spiral waves between the layers across these various stimulus parameters, as well as for different intralayer coupling coefficients. Finally, the trend of synchronization between the two layers is investigated using the spatial interlayer synchronization error across a range of interlayer coupling strengths. The important findings of the present study are discussed in the conclusion.

Keywords: memristor, Morris-Lecar neuron, spatiotemporal dynamics, spiral waves