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Impulsive Multisynchronization of Coupled Multistable Neural Networks With Time-Varying Delay
IEEE Transactions on Neural Networks and Learning Systems
|April 13, 2016
Summary
This study addresses synchronization in coupled delayed multistable neural networks (NNs). New methods achieve dynamical multisynchronization (DMS) and static multisynchronization (SMS) in NNs with complex network topologies.
Area of Science:
- Computational Neuroscience
- Network Dynamics
- Control Theory
Background:
- Multistable neural networks (NNs) exhibit complex dynamics with multiple stable states.
- Synchronization is crucial for information processing in NNs.
- Coupled NNs with time delays and directed topologies present significant theoretical challenges.
Purpose of the Study:
- To investigate the synchronization problem in coupled delayed multistable NNs with directed topology.
- To introduce and define novel synchronization concepts: dynamical multisynchronization (DMS) and static multisynchronization (SMS).
- To develop control strategies for achieving DMS and SMS in these complex network systems.
Main Methods:
- Development of sufficient conditions using algebraic inequalities for subnetwork stability.
- Introduction of impulsive control strategies.
- Application of Razumikhin-type techniques for analyzing delayed systems.
- Analysis of both fixed and switching network topologies.
Main Results:
- Sufficient conditions are established ensuring multiple stable periodic orbits or equilibrium points in subnetworks.
- Novel synchronization manifolds, DMS and SMS, are formally defined.
- Effective control conditions are derived for achieving both DMS and SMS in controlled coupled delayed multistable NNs.
- The proposed methods are validated through simulation examples.
Conclusions:
- The study successfully establishes conditions for achieving novel forms of synchronization (DMS and SMS) in complex neural network systems.
- Impulsive control and Razumikhin-type techniques are effective for managing synchronization in delayed multistable NNs.
- The findings contribute to understanding and controlling complex dynamics in artificial neural networks.
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