The influence of spatial configuration in collective transitions: the importance of being sorted

TL;DR

This study investigates how the spatial arrangement of heterogeneous nodes in a network influences the ease of transition to synchronized oscillatory activity, revealing that increased sortedness lowers the required network drive.

Contribution

It introduces an iterative algorithm to increase network sortedness and demonstrates its impact on collective dynamics and transition thresholds in coupled lattice networks.

Findings

Higher sortedness reduces the network drive needed for synchronization.

Partial synchronization regimes depend on both network drive and sortedness.

Sortedness influences the emergence of resonance phenomena in the network.

Abstract

We studied the effects of spatial configuration on collective dynamics in a nearest-neighbour and diffusively coupled lattice of heterogeneous nodes. The networks contained nodes from two populations, which differed in their intrinsic excitability. Initially, these populations were uniformly and randomly distributed throughout the lattice. We then developed an iterative algorithm for perturbing the arrangement of the network such that nodes from the same population were increasingly likely to be adjacent to one another. We found that the global input strength, or network drive, necessary to transition the network from a state of quiescence to a state of synchronised and oscillatory activity was decreased as network sortedness was increased. Moreover, for weak coupling, we found that regimes of partial synchronisation exist (i.e., 2:1 resonance in the activity of the two populations), which were dependent both on network drive (sometimes in a non-monotonic fashion) and network sortedness.