具有不连续激活函数和时滞的分数阶Hopfield神经网络

Fractional-Order Hopfield Neural Networks with Discontinuous Activation Functions and Time Delays

摘要: 近年来，神经网络广泛运用于图像处理、模式识别、诊断故障、以及通信保密等各个复杂领域。神经网络系统的运用主要依赖其稳定性。在实际应用中，时滞现象经常发生，若能够充分利用时滞现象，对于提高系统的稳定性是很有帮助的。由于分数阶神经网络有着更好的记忆特性与遗传特性，因此，本文注重对分数阶时滞神经网络的稳定性进行研究。对具有不连续激活函数的Caputo分数阶时滞神经网络模型进行了研究。不同于其他文章，本文研究的激活函数是不连续的，更加贴合实际情况。在Filippov意义下，提出了能够保证系统解存在的条件，同时对平衡点的渐近稳定性做了探讨。此外还提出来了一个钉扎同步控制策略，与其他的同步条件不同，在一个很小的范围内，保证在合适的条件下，主从系统实现准同步。最后，通过数值例子以及仿真模拟说明所得结果的有效性。

Abstract: In recent years, neural networks have been widely used in various complex fields such as image processing, pattern recognition, fault diagnosis, and communication security. The application of neural network systems mainly relies on their stability. In practical applications, time delay phenomena often occur. If time delay phenomena can be fully utilized, it is very helpful to improve the stability of the system. Due to the better memory and genetic characteristics of fractional order neural networks, this article focuses on exploring the stability of fractional order delay neural networks. Caputo fractional delayed neural network model with discontinuous activation function is studied. Different from other articles, the activation function studied in this paper is discontinuous and more practical. In the sense of Filippov, conditions were proposed to ensure the existence of system solutions, and the asymptotic stability of equilibrium points was explored. In addition, a pinning synchronization control strategy has been proposed, which is different from other synchronization conditions and ensures that the master slave system achieves quasi synchronization under suitable conditions within a very small range. Finally, numerical examples and simulation simulations are used to demonstrate the effectiveness of the obtained results.