Global synchronization of coupled delayed memristive reaction-diffusion neural networks

Area of Science:

• Complex Systems
• Nonlinear Dynamics
• Computational Neuroscience

Background:

• Traditional neural networks often simplify circuit realization and omit spatial influences.
• Memristive neural networks offer more realistic modeling due to memristor properties.
• Time delays are crucial in modeling real-world neural network dynamics.

Purpose of the Study:

• To investigate the global exponential synchronization of multiple memristive reaction-diffusion neural networks (MRDNNs) with time delays.
• To develop robust synchronization criteria for MRDNNs under various coupling configurations.
• To validate the theoretical results through numerical simulations.

Main Methods:

• Lyapunov functional theory for stability analysis.
• Divergence theorem for spatial dynamics.
• Inequality techniques to establish synchronization criteria.
• Analysis of both directed and undirected nonlinear coupling schemes.

Main Results:

• Derivation of global exponential synchronization criteria for coupled delayed MRDNNs.
• Demonstration of synchronization under both directed and undirected coupling.
• Validation of the derived criteria through three numerical simulation examples.

Conclusions:

• The proposed methods effectively achieve global exponential synchronization for MRDNNs.
• The derived criteria are applicable to a more general and realistic class of neural networks.
• Numerical simulations confirm the theoretical findings and the feasibility of the approach.