Distributed synchronization of coupled neural networks via randomly occurring control

Area of Science:

• Control Theory
• Network Science
• Computational Neuroscience

Background:

• Stochastic complex networks, particularly neural networks, present challenges in achieving synchronized behavior due to inherent randomness.
• Distributed control strategies are crucial for managing large-scale networks where centralized control is infeasible.

Purpose of the Study:

• To investigate the distributed synchronization and distributed pinning synchronization of stochastic coupled neural networks using randomly occurring control.
• To analyze the effectiveness and implementation feasibility of this control strategy compared to alternatives.

Main Methods:

• Utilizing two Bernoulli stochastic variables to model the probabilistic occurrence of control actions and updating laws.
• Employing Lyapunov functions and stochastic analysis techniques to rigorously prove synchronization criteria.
• Analyzing state information dependency on network neighborhoods for distributed control design.

Main Results:

• The proposed randomly occurring control strategy successfully achieves distributed synchronization and distributed pinning synchronization in mean square.
• The control method is shown to be more practical and less restrictive than periodically intermittent control.
• Convergence rates and control costs are analyzed, positioning randomly occurring control as a balanced approach.

Conclusions:

• Randomly occurring control is an effective and implementable method for achieving synchronization in stochastic coupled neural networks.
• This approach provides a valuable alternative to traditional control methods, offering a practical balance between performance and ease of application.
• The findings contribute to the advancement of control theory for complex dynamical systems.