Dynamical and static multisynchronization analysis for coupled multistable memristive neural networks with hybrid...

Area of Science:

• Neuroscience
• Control Theory
• Complex Systems

Background:

• Memristive neural networks exhibit complex dynamics with multiple stable states.
• Achieving synchronization in such networks, especially with delays, is challenging.
• Multistable systems require advanced control strategies for coordinated behavior.

Purpose of the Study:

• To investigate dynamical multisynchronization (DMS) and static multisynchronization (SMS) in delayed coupled multistable memristive neural networks (DCMMNNs).
• To develop and validate a novel hybrid controller for achieving DMS and SMS.
• To establish sufficient conditions for synchronization using linear matrix inequalities (LMIs).

Main Methods:

• Utilizing a hybrid controller combining delayed impulsive control and state feedback control.
• Applying state-space partition and analysis of activation function properties.
• Employing a novel Halanay-type inequality and impulsive control theory.
• Deriving LMI-based conditions for synchronization.

Main Results:

• The proposed hybrid controller effectively achieves DMS and SMS in DCMMNNs.
• Sufficient conditions for synchronization are established using LMIs.
• The controller's effectiveness is demonstrated even with time-varying delays and specific impulsive intervals.
• A numerical example validates the theoretical findings.

Conclusions:

• The novel hybrid controller is effective for synchronizing DCMMNNs.
• Delayed impulsive control can successfully manage synchronization in complex neural networks.
• The LMI-based conditions provide a robust framework for analyzing network stability and synchronization.