Year: 2026
Type: preprint
Abstract: We introduce a novel coupling of Rulkov neural maps, proposing a heuristic biological interpretation for the transition to non-small values of the perturbations acting on the slow variables. We analytically prove that the coupling of two identical neurons preserves the emergence of Devaney chaos through the existence of a generalized snap-back repeller, provided that a snap back repeller exists for the original system. We present numerical simulations for the coupling of two different neurons showing the arising of a potential global strange attractor, whose fractal structure is strongly suggested by the computation of a non-integer Kaplan-Yorke dimension. Furthermore, we perform standard numerical studies concerning time series, Lyapunov exponents spectra, bifurcation diagrams and basins of attraction. Finally, we briefly propose a generalization of the coupling to an arbitrary number of neurons.
Source: arXiv (Cornell University)
Author: Disca, Stefano
Institution: University of Ferrara
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Award: G364684122
OpenAlex ID: W7171428426