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Bipartite Synchronization for Coupled Fractional-Order Reaction-Diffusion Neural Networks With Multiple Weights.
This study achieves bipartite synchronization in coupled fractional-order reaction-diffusion neural networks (CFRNN) using adaptive control. The research provides conditions for both multiple state and multiple spatial diffusion CFRNN models.
Area of Science:
- Control Theory
- Neural Networks
- Fractional Calculus
Background:
- Coupled fractional-order reaction-diffusion neural networks (CFRNN) are complex systems with applications in various fields.
- Achieving synchronization in these networks is crucial for their coordinated behavior.
Purpose of the Study:
- To investigate and achieve bipartite synchronization in CFRNN with multiple state or multiple spatial diffusion couplings.
- To develop control strategies for ensuring bipartite synchronization in these complex networks.
Main Methods:
- Lyapunov functional method combined with inequality techniques.
- Development of an adaptive state-feedback control scheme.
- Derivation of sufficient conditions for bipartite synchronization.
Main Results:
- A bipartite synchronization condition is derived for multiple state CFRNN (MSCFRNN).
- An adaptive state-feedback control scheme is proposed for MSCFRNN.
- Sufficient conditions are established for bipartite synchronization in multiple spatial diffusion CFRNN (MSDCFRNN).
Conclusions:
- The proposed control strategies effectively ensure bipartite synchronization in both MSCFRNN and MSDCFRNN.
- Numerical examples validate the theoretical findings and the effectiveness of the control methods.
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