Coevolution of Glauber-like Ising dynamics on typical networks

TL;DR

This paper investigates how the coevolution of node states and network structure affects system stability and magnetization, comparing different initial network topologies and parameters.

Contribution

It introduces a model of Glauber-like Ising dynamics on evolving networks and analyzes the impact of initial topology and parameters on steady states.

Findings

Steady state stability is similar across different initial networks.

Magnetization varies depending on initial network conditions.

Parameters S and φ significantly influence the steady-state behavior.

Abstract

We consider coevolution of site status and link structures from two different initial networks: a one dimensional Ising chain and a scale free network. The dynamics is governed by a preassigned stability parameter $S$, and a rewiring factor $\phi$, that determines whether the Ising spin at the chosen site flips or whether the node gets rewired to another node in the system. This dynamics has also been studied with Ising spins distributed randomly among nodes which lie on a network with preferential attachment. We have observed the steady state average stability and magnetisation for both kinds of systems to have an idea about the effect of initial network topology. Although the average stability shows almost similar behaviour, the magnetisation depends on the initial condition we start from. Apart from the local dynamics, the global effect on the dynamics has also been studied. These parameters show interesting variations for different values of $S$ and $\phi$, which helps in determining the steady-state condition for a given substrate.