Memristive field effect in a single and multilayer neural network with different connection topologies

The network connectivities play an important role in displaying the vastly different collective dynamics in many complex systems. To demonstrate the presence of different dynamical states and their transition, we consider Hindmarsh-Rose neurons, which are linked up by electromagnetic interactions. The dynamical behaviors of the proposed system are specifically explored under three distinct network connectivities: Regular(RG), small-world (SW), and random (RAND) interactions. We discover that increasing coupling intensity illustrates the dynamical transition from the desynchronization state to the traveling wave state for all the considered network interactions. Particularly, the regular network shows the emergence of spatial symmetric patterns that transit to a homogeneous steady state while increasing the strength of magnetic field interaction. In addition, the transition from an asymmetric pattern to an in-homogeneous steady state is noticed for small-world and random networks. The investigation is then extended to a three-layer multiplex network in which nodes interact electromagnetically within (intra-) layers and magnetically between (inter-) layers, since many complex networks in the real world have large numbers of nodes organized (or located) in different subnetworks. We show that increasing the coupling intensity leads to synchronization in all layers and, eventually, a rest state at high coupling strength.