The emergence of pseudo-stable states in network dynamics

TL;DR

This paper investigates network dynamics under Heider balance theory, revealing pseudo-deterministic paths leading systems to jammed and balanced states, with the Inverse Participation Ratio serving as an effective indicator of these collective behaviors.

Contribution

It introduces the use of the Inverse Participation Ratio to predict pseudo-deterministic paths in network evolution towards specific states.

Findings

Inverse Participation Ratio indicates collective behavior in network paths.

Paths to jammed states are not random but follow predictable patterns.

Proximity to final states constrains the system's evolution.

Abstract

In the context of network dynamics, the complexity of systems increases possible evolutionary paths that often are not deterministic. Occasionally, some map routs form over the course of time which guide systems towards some particular states. The main intention of this study is to discover an indicator that can help predict these pseudo-deterministic paths in advance. Here we investigate the dynamics of networks based on Heider balance theory that states the tendency of systems towards decreasing tension. This inclination leads systems to some local and global minimum tension states called "jammed states" and "balanced states", respectively. We show that not only paths towards jammed states are not completely random but also there exist secret pseudo deterministic paths that bound the system to end up in these special states. Our results display that the Inverse Participation Ratio method (IPR) can be a suitable indicator that exhibits collective behaviors of systems. According to this method, these specific paths are those that host the most participation of the constituents in the system. A direct proportionality exists between the distance and the selectable paths towards local minimums; where by getting close to the final steps there is no other way but the one to the jammed states.