Excitable media store and transfer complicated information via topological defect motion

Sudakow, Ivan; Vakulenko, Sergey A. and Grigoriev, Dmitry (2023). Excitable media store and transfer complicated information via topological defect motion. Communications in Nonlinear Science and Numerical Simulation, 116, article no. 106844.

DOI: https://doi.org/10.1016/j.cnsns.2022.106844

Abstract

Excitable media are prevalent models for describing interesting effects in physical, chemical, and biological systems such as pattern formation, chaos, and wave propagation. In this manuscript, we propose a spatially extended variant of the FitzHugh–Nagumo model that exhibits new effects. In this excitable medium, waves of new kinds propagate. We show that the time evolution of the medium state at the wavefronts is determined by complicated attractors which can be chaotic. The dimension of these attractors can be large and we can control the attractor structure by initial data and a few parameters. These waves are capable transfer complicated information given by a Turing machine or associative memory. We show that these waves are capable to perform cell differentiation creating complicated patterns.

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