Synchronization in a temporal multiplex neuronal hypernetwork

Synchronization in time-varying complex dynamical systems has been explored in a variety of different coupling topologies during the last two decades. In most of the previous cases, the basic time-varying coupling topologies were considered to be a single interaction between the nodes or in a monolayer configuration, although in many real situations the types of interactions are more than one or in the form of multilayer. In this work, we study the synchronization in multiplex neuronal network, which evolves with time, and each layer consists of more than one interaction function. Specifically, we consider a neuronal hypernetwork at each layer in which neurons are communicated with each other via electrical and chemical synapses simultaneously and independently. The network corresponding to the electrical gap junctional coupling form a small-world network while the connection associated with the chemical synaptic interaction forms a unidirectional random network. Then intralayer connections are allowed to switch stochastically over time with a characteristic rewiring frequency, whereas interlayer connections via electrical synapses are time invariant. We explore the intralayer and interlayer neuronal synchrony in such network and analytically derive the necessary stability conditions for synchrony using master stability function approach, and excellently match with our numerical findings. Interestingly, we find that the higher frequency of switching links in the intralayer enhances both intralayer and interlayer synchrony and conferring larger windows of synchrony. We also analyze the robustness of these synchronization states with respect to initial conditions using the basin stability framework. Furthermore we find that rapidly changing networks take much less time to reach synchronization state. Lastly, we inspect the dynamical robustness of interlayer synchronization against stochastic demultiplexing of each replica, with analytical justification.