Coupling-modulated multi-stability and coherent dynamics in directed networks of heterogeneous nonlinear oscillators with modular topology

We discuss the dynamics of modular networks of coupled nonlinear systems. Networks of this class can be viewed as locally connected clusters or modules of nodes with directed links from one cluster to another. Let these connections form an oriented cycle. Here we show that if connectivity within isolated clusters is diffusive with relatively strong coupling, then spectral properties of the corresponding network coupling matrix promote emergence and co-existence of multiple coherent and orderly dynamic regimes. We hypothesise that, similar to our previous work on the dynamics of cycles, in addition to a nearly fully synchronous state, an attracting rotating wave solution may occur. Furthermore, prevalence of one solution type over the other could be determined by the combination of the cycle length, inter- and intra-cluster coupling strengths, and the number of elements in each module. Our preliminary numerical experiments support these hypotheses.