Collective behavior of an adapting synapse-based neuronal network with memristive effect and randomness.

This study delves into the examination of a network of adaptive synapse neurons characterized by a small-world network topology connected through electromagnetic flux and infused with randomness. First, this research extensively explores the existence of the global multi-stability of a single adaptive synapse-based neuron model with magnetic flux. The non-autonomous neuron model exhibits periodically switchable equilibrium states that are strongly related to the transitions between stable and unstable points in every whole periodic cycle, leading to the creation of global multi-stability. Various numerical measures, including bifurcation plots, phase plots, and basin of attraction, illustrate the intricate dynamics of diverse coexisting global firing activities. Moreover, the model is extended by coupling two neurons with a memristive synapse. The dynamics of the coupled neurons model are showcased with the help of largest Lyapunov exponents, and synchronized dynamics are viewed with the help of mean average error. Next, we consider a regular network of neurons connected to their nearest neighbors through the memristive synapse. We then reconstruct it into a small-world network by increasing the randomness in the rewiring links. Consequently, we observed collective behavior influenced by the number of neighborhood connections, coupling strength, and rewiring probability. We used spatio-temporal patterns, recurrence plots, as well as global-order parameters to verify the reported results.