Regulating synchronous states of complex networks by pinning interaction with an external node

Area of Science:

• Complex systems
• Network dynamics
• Control theory

Background:

• Biological and technological systems often rely on synchronized functioning.
• Understanding how to engineer synchronization in networks is crucial for various applications.
• External interventions can influence network behavior, but methods for controlled synchronization are needed.

Purpose of the Study:

• To investigate methods for engineering external control to achieve synchronous functioning in networks of dynamical units.
• To develop a strategy for regulating network behavior toward synchronization using a bidirectional interaction with an external node.
• To identify network properties that make them susceptible to external regulation for synchronization.

Main Methods:

• Modeling a network of dynamical units interacting with an external node.
• Developing a bidirectional interaction strategy where the external node's parameters remain unchanged.
• Analyzing network susceptibility to external regulation and designing pinning sequences.
• Comparing the designed pinning sequences with network topological rankings.

Main Results:

• Demonstrated that two distinct classes of networks can be regulated into synchronous motion.
• Provided specific, simple methods for designing effective pinning sequences for each network class.
• Showcased that external regulation can achieve synchronized behavior without altering the internal network structure.
• Established a framework for comparing control sequences with network topology.

Conclusions:

• External pinning actions can effectively engineer and maintain synchronous functioning in specific types of dynamical networks.
• The developed methods offer practical approaches for controlling network synchronization.
• The findings contribute to the broader understanding of network dynamics and control in both natural and artificial systems.