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Bipartite synchronization in coupled delayed neural networks under pinning control
Fang Liu1, Qiang Song2, Guanghui Wen3
1School of Information Engineering, Huanghuai University, Zhumadian, Henan 463000, China.
Summary
This study achieves bipartite leader-following synchronization in signed neural networks using pinning control. It establishes conditions for synchronization with bounded, differentiable, and non-differentiable delays.
Area of Science:
- Control Theory
- Network Science
- Computational Neuroscience
Background:
- Signed networks feature both positive and negative connections, posing unique synchronization challenges.
- Leader-following synchronization is crucial for coordinated behavior in complex systems.
- Coupled delayed neural networks are fundamental models in understanding brain dynamics.
Purpose of the Study:
- To investigate bipartite leader-following synchronization in signed networks of coupled delayed neural networks.
- To develop control strategies for achieving synchronization under various delay conditions.
- To establish theoretical conditions and practical methods for synchronization analysis.
Main Methods:
- Utilizing pinning control strategy and M-matrix theory for network control.
- Deriving conditions based on linear matrix inequalities (LMIs) for differentiable delays.
- Applying descriptor systems and the reciprocally convex approach for non-differentiable delays.
Main Results:
- A sufficient condition for bipartite leader-following synchronization in signed networks with bounded, differentiable delays was derived.
- An algebraic formula was developed to estimate the upper bound of node-delay.
- Criteria were established to solve the synchronization problem for bounded, non-differentiable delays.
Conclusions:
- The proposed methods effectively achieve bipartite leader-following synchronization in signed networks of coupled delayed neural networks.
- The theoretical findings are validated through numerical simulations, demonstrating practical applicability.
- The study contributes robust control strategies for synchronization in complex, signed, and delayed network systems.
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