具有混合耦合和时变延迟的线性耦合反应扩散神经网络的同步问题通过非周期性间断定控方法
Synchronization of linearly coupled reaction-diffusion neural networks with hybrid coupling and time-varying delays via aperiodically intermittent pinning control
AI总结：
本文研究了通过非周期性间断定控方法实现具有反应扩散项和时变延迟的线性耦合神经网络的完全同步问题，提出了一种新的分布式耦合协议，提高了同步速度，并通过数值模拟验证了理论结果。
摘要：
本文研究了通过非周期性间断定控方法实现具有反应扩散项和时变延迟的线性耦合神经网络的完全同步问题。网络耦合矩阵可以是不对称的。与同步文献中的状态耦合不同，我们设计了一种新的分布式耦合协议，利用反应扩散耦合-空间耦合，从而加速同步过程。这可以视为本文与以往工作的主要区别。利用Lyapunov函数和非周期性间断控制理论，我们提出了某些关于静态耦合强度的完全同步准则。在这种情况下，时变延迟的界没有限制，因此可以大于控制跨度的长度。另一方面，对于具有自适应耦合强度的网络，我们提出了一种简单的自适应规则用于耦合强度，并严格证明了其有效性。在这种情况下，时变延迟的界需要小于控制时间跨度的下确界。最后，给出了数值模拟以验证理论结果。
英文摘要：
In this paper, the complete synchronization problem of linearly coupled neural networks with reaction-diffusion terms and time-varying delays via aperiodically intermittent pinning control is investigated. The coupling matrix for the network can be asymmetric. Compared with state coupling in the synchronization literature, we design a novel distributed coupling protocol by using the reaction-diffusion coupling-spatial coupling, which can accelerate the synchronization process. This can be regarded as the main difference between this paper and previous works. Using the Lyapunov function and theories in the aperiodically intermittent control, we present some criteria for the complete synchronization with a static coupling strength. In this case, there is no constraint on the bound of time-varying delays, so it can be larger than the length of control span. On the other hand, for the network with an adaptive coupling strength, we propose a simple adaptive rule for the coupling strength and prove its effectiveness rigorously. In this case, the bound of time-varying delay is required to be less than the infimum of the control time span. Finally, numerical simulations are given to verify the theoretical results.
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