Hierarchical-dependent cluster synchronization in directed networks with semiconductor lasers.

Area of Science:

• Physics
• Nonlinear Dynamics
• Complex Networks

Background:

• Cluster synchronization in complex networks is a key area of research.
• Previous studies primarily focused on undirected networks.
• Semiconductor lasers (SLs) are common elements in complex network synchronization studies.

Purpose of the Study:

• To numerically investigate complete cluster synchronization in directed networks of semiconductor lasers.
• To analyze the influence of semiconductor laser and network parameters on synchronization.
• To identify hierarchical dependencies in cluster synchronization stability within directed networks.

Main Methods:

• Numerical simulations of coupled semiconductor laser systems.
• Analysis of cluster synchronization patterns in directed network topologies.
• Investigation of parameter dependencies for synchronization formation and stability.

Main Results:

• Complete cluster synchronization is achievable in directed networks of semiconductor lasers.
• Semiconductor laser parameters and network parameters significantly impact synchronization.
• A hierarchical dependency exists between the synchronization stability of different clusters, where one cluster's stability can affect another, but not vice versa.

Conclusions:

• Directed network topology introduces unique dynamics to cluster synchronization.
• Parameter control is crucial for achieving and maintaining desired synchronization patterns.
• The hierarchical nature of synchronization stability in directed networks offers new insights for network design and control.