Two-cluster synchronization in a fully coupled network of Mackey–Glass generators

Abstract

We study a fully connected network of Mackey–Glass generators, each described by the Mackey–Glass delay differential equation. This system can exhibit non-trivial behaviour over time. One interesting scenario of such behaviour is cluster synchronization—regimes in which all components are divided into several groups, each oscillating in the same mode. Cluster synchronization can appear in various systems, such as neural networks and biological systems. In this work, we investigate the case of two-cluster synchronization and prove the existence of such modes.

Keywords

• Mackey–Glass equation
• Cluster synchronization
• Periodical solution
• Delay differential equation