Synchronization of Complex Dynamical Networks with Stochastic Links Dynamics.

Area of Science:

• Complex Systems
• Network Science
• Stochastic Systems

Background:

• Complex dynamical networks (CDNs) exhibit intricate behaviors influenced by both node and link dynamics.
• Existing research often overlooks the stochastic nature of link evolution within CDNs.
• Understanding and controlling these stochastic dynamics is crucial for network stability and function.

Purpose of the Study:

• To investigate the mean square synchronization problem in complex dynamical networks (CDNs) with stochastic link dynamics.
• To propose a novel control strategy that addresses both node and link subsystem dynamics.
• To demonstrate the asymptotic tracking of a stochastic reference signal by the network links.

Main Methods:

• Modeling the CDN as two coupled subsystems: a nodes subsystem and a network topology subsystem.
• Utilizing two vector stochastic differential equations with Brownian motion to represent the dynamics of nodes and links.
• Developing a control strategy that integrates controllers within nodes and coupling terms within links.

Main Results:

• Achieved mean-square synchronization of the CDN by simultaneously controlling nodes and links.
• Introduced a dynamic stochastic signal for links to track, ensuring asymptotic convergence.
• Demonstrated that the control strategy leads to a stochastic eventual topological structure for the CDN.
• Simulation results confirmed the effectiveness and superiority of the proposed control strategy.

Conclusions:

• The proposed control strategy effectively achieves mean-square synchronization in complex dynamical networks with stochastic link dynamics.
• The integration of link dynamics control and a stochastic reference signal enables predictable network behavior and a stochastic topology.
• This approach offers a robust method for controlling complex systems with inherent randomness and evolving structures.