Exponential Synchronization of Coupled Stochastic Memristor-Based Neural Networks With Time-Varying Probabilistic Delay Coupling and Impulsive Delay

Area of Science:

• Complex Systems
• Computational Neuroscience
• Nonlinear Dynamics

Background:

• Memristor-based neural networks (MNNs) are crucial for advanced computing.
• Stochasticity and time-varying delays introduce significant challenges in MNN synchronization.
• Impulsive effects further complicate the stability analysis of these networks.

Purpose of the Study:

• To investigate the exponential synchronization of coupled stochastic MNNs.
• To address the complexities of probabilistic time-varying delay coupling and impulsive delays.
• To develop robust theoretical conditions for achieving synchronization in these intricate systems.

Main Methods:

• Utilized Lyapunov functions for stability analysis.
• Applied the Halanay inequality to handle time delays.
• Employed linear matrix inequalities (LMIs) for deriving sufficient conditions.
• Incorporated stochastic variables (Bernoulli) to model probabilistic delays.

Main Results:

• Derived sufficient conditions for exponential synchronization.
• Demonstrated that synchronization depends on the probability distribution of delays and impulsive intervals.
• Confirmed the effectiveness of the proposed theoretical framework through numerical simulations.

Conclusions:

• The developed criteria ensure exponential synchronization for the studied MNNs.
• The methodology effectively accounts for stochastic and probabilistic delay factors.
• Numerical simulations validate the theoretical results, highlighting practical applicability.