Nonlinear network dynamics under perturbations of the underlying graph

TL;DR

This paper explores how changes in network connectivity, such as edge weights and configurations, influence the dynamics and bifurcations of coupled nonlinear oscillators, with implications for understanding brain and neural networks.

Contribution

It provides a detailed analysis of how various perturbations to the underlying graph affect the phase space and bifurcation structure of nonlinear oscillator networks, incorporating randomness.

Findings

Connectivity perturbations alter bifurcation structures

Edge modifications impact network dynamics significantly

Results have implications for neural and brain networks

Abstract

Many natural systems are organized as networks, in which the nodes (be they cells, individuals or populations) interact in a time-dependent fashion. The dynamic behavior of these networks depends on how these nodes are connected, which can be understood in terms of an adjacency matrix, and connection strengths. The object of our study is to relate connectivity to temporal behavior in networks of coupled nonlinear oscillators. We investigate the relationship between classes of system architectures and classes of their possible dynamics, when the nodes are coupled according to a connectivity scheme that obeys certain constrains, but also incorporates random aspects. We illustrate how the phase space dynamics and bifurcations of the system change when perturbing the underlying adjacency graph. We differentiate between the effects on dynamics of the following operations that directly modulate network connectivity: (1) increasing/decreasing edge weights, (2) increasing/decreasing edge density, (3) altering edge configuration by adding, deleting or moving edges. We discuss the significance of our results in the context of real life networks. Some interpretations lead us to draw conclusions that may apply to brain networks, synaptic restructuring and neural dynamics.