On Self-Organized Criticality and Synchronization in Lattice Models of Coupled Dynamical Systems

TL;DR

This paper reviews how lattice models of coupled dynamical systems exhibit complex behaviors like self-organized criticality, synchronization, clustering, and phase-locking, depending on specific conditions.

Contribution

It provides a comprehensive review of conditions leading to various complex behaviors in models of coupled oscillators and stick-slip processes.

Findings

Identification of conditions for self-organized criticality

Analysis of clusterization and phase-locking phenomena

Comparison of behaviors in different lattice models

Abstract

Lattice models of coupled dynamical systems lead to a variety of complex behaviors. Between the individual motion of independent units and the collective behavior of members of a population evolving synchronously, there exist more complicated attractors. In some cases, these states are identified with self-organized critical phenomena. In other situations, with clusterization or phase-locking. The conditions leading to such different behaviors in models of integrate-and-fire oscillators and stick-slip processes are reviewed.