On a cross coupling of Rulkov neural maps

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 preserves boundedness of motion and the existence of a snap-back repeller (leading to Devaney chaos by the Marotto theorem), if they are associated to the original system. For the coupling of two standard chaotic Rulkov maps, we present numerical simulations for the orbits of the system showing the arising of a 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:2607.22318v1 - http://arxiv.org/abs/2607.22318v1 PDF: https://arxiv.org/pdf/2607.22318v1 Original Link: http://arxiv.org/abs/2607.22318v1