Synchronization of multiplex and directed reaction-diffusion neural networks with hybrid coupling

Area of Science:

• Complex Systems
• Computational Neuroscience
• Network Science

Background:

• Synchronization is crucial for the function of many complex systems, including neural networks.
• Existing models often assume simplified network structures (symmetric, strongly connected matrices).
• Multiplex and directed reaction-diffusion neural networks (MDHCRDNN) present unique synchronization challenges due to hybrid coupling and complex matrix properties.

Purpose of the Study:

• To develop a novel approach for achieving exponential synchronization in MDHCRDNN with hybrid coupling.
• To address synchronization in networks with asymmetric, competitive, and disconnected outer matrices, and negative inner matrix elements.
• To investigate hybrid control and adaptive strength for enhanced synchronization.

Main Methods:

• A novel approach transforming state coupling into spatial coupling.
• Integration of spatial diffusion and state matrices into new combined matrices.
• Analysis of network synchronization based on the connectivity of these combined matrices.

Main Results:

• Synchronization can be guaranteed exponentially under specific conditions of matrix connectivity.
• The proposed method effectively handles asymmetric, competitive, and disconnected outer matrices.
• Successful resolution of hybrid control and adaptive strength issues.

Conclusions:

• The developed method provides a robust framework for synchronizing complex MDHCRDNN.
• The findings extend the understanding of synchronization in networks with challenging coupling structures.
• Simulations confirm the effectiveness and practical applicability of the derived results.