Cluster Synchronization for Neutral Stochastic Delay Networks via Intermittent Adaptive Control

Area of Science:

• Complex Systems and Networks
• Nonlinear Dynamics and Control
• Stochastic Systems and Probability Theory

Background:

• Neutral stochastic coupled neural networks with time-varying delays present significant control challenges.
• Achieving cluster synchronization at exponential rates is crucial for distributed information processing.
• Existing control strategies often struggle with the combined effects of stochasticity, neutral items, and time delays.

Purpose of the Study:

• To investigate and achieve exponential cluster synchronization for neutral stochastic coupled neural networks.
• To develop a periodically intermittent pinning adaptive control strategy for enhanced network stability.
• To analyze synchronization performance in both mean square and almost sure senses.

Main Methods:

• Application of a periodically intermittent pinning adaptive control strategy.
• Utilizing the delay integral inequality approach for mean square exponential stabilization.
• Employing the nonnegative semimartingale convergence theorem for almost sure exponential stabilization.

Main Results:

• Sufficient criteria for achieving exponential cluster synchronization in both mean square and almost sure senses were derived.
• The proposed control strategy effectively manages the complexities of neutral items, stochastic disturbances, and time-varying delays.
• Demonstrated the effectiveness of the theoretical results through two illustrative examples.

Conclusions:

• The developed adaptive control strategy guarantees exponential cluster synchronization for the studied neural networks.
• The methodology provides a robust framework for analyzing and controlling complex stochastic systems with delays.
• The findings contribute to the advancement of synchronization theory in neural networks and complex dynamical systems.