Dynamical and Static Multisynchronization of Coupled Multistable Neural Networks via Impulsive Control

Area of Science:

• Complex Systems
• Computational Neuroscience
• Control Theory

Background:

• Multistable neural networks exhibit multiple equilibrium states, crucial for complex dynamics.
• Synchronization in delayed networks with fixed and switching topologies is challenging.
• Impulsive control offers a method for stabilizing and synchronizing dynamical systems.

Purpose of the Study:

• Investigate dynamical and static multisynchronization in delayed multistable neural networks.
• Develop conditions ensuring multiple equilibrium states within subnetworks.
• Design a unified impulsive controller for achieving multisynchronization.

Main Methods:

• Introduced novel activation functions and sufficient conditions for multistability.
• Employed Lyapunov functions and impulsive control theory.
• Utilized the average impulsive interval method and linear matrix inequalities (LMIs).

Main Results:

• Derived sufficient conditions for multisynchronization expressed via LMIs.
• Established a unified impulsive controller based on LMIs.
• Demonstrated the effectiveness of the impulsive control strategy through a numerical example.

Conclusions:

• The proposed impulsive control strategy effectively achieves multisynchronization in delayed multistable neural networks.
• The derived LMIs provide a systematic approach for designing controllers.
• The study contributes to understanding and controlling complex neural network dynamics.