Pinning-controlled synchronization of delayed neural networks with distributed-delay coupling via impulsive control

Area of Science:

• Computational Neuroscience
• Control Theory
• Network Science

Background:

• Coupled neural networks are essential models in neuroscience and artificial intelligence.
• Achieving synchronization in complex networks with delays and varied topologies presents significant challenges.
• Impulsive control is a powerful technique for stabilizing and synchronizing dynamical systems.

Purpose of the Study:

• To investigate pinning synchronization in coupled neural networks with current-state and distributed-delay coupling.
• To propose a novel impulse pinning strategy incorporating a pinning ratio.
• To derive general and low-dimensional criteria for achieving synchronization in diverse network topologies.

Main Methods:

• Development of a novel impulse pinning strategy with a pinning ratio.
• Derivation of synchronization criteria using inequality techniques.
• Application of matrix decomposition methods (simultaneous diagonalization) for dimensionality reduction.
• Analysis of coupled neural networks with both current-state and distributed-delay coupling.

Main Results:

• A general criterion for pinning synchronization is established for coupled neural networks.
• Low-dimensional criteria are obtained by overcoming high-dimensional challenges.
• The proposed impulse pinning strategy effectively ensures synchronization across networks with different topologies.
• An illustrative example demonstrates the practical effectiveness of the developed method.

Conclusions:

• The proposed impulse pinning strategy is effective for achieving synchronization in complex coupled neural networks.
• The derived low-dimensional criteria simplify the analysis and implementation of synchronization control.
• This work contributes to the understanding and control of synchronization phenomena in dynamical systems.