Abstract:
In this paper, we study intralayer synchronization of multiplex networks where nodes in each layer
interact through diverse types of coupling functions associated with different time-varying network
topologies, referred to as multiplex hypernetworks. Here, the intralayer connections are evolving
with respect to time, and the interlayer connections are stagnant. In this context, an interesting
and important problem is to analyze the stability of the intralayer synchronization in such temporal
networks. We prove that if the dynamical multiplex hypernetwork for the time-average topology
possesses intralayer synchronization, then each layer of the time-varying multiplex hypernetwork will
also be synchronized for sufficiently fast switching. Then through master stability function formalism,
we analytically derive necessary and sufficient stability conditions of intralayer synchronous states
for such temporal architecture in terms of a time-average network. In this regard, we are able to
decouple the transverse error component of the intralayer synchronization states for some special
cases. Also, we extend our study for nonlinear intralayer coupling functions as well as multilayer
hypernetwork architectures. Finally, the theoretical findings are verified numerically by taking the
network of paradigmatic chaotic R\"ossler oscillators.
