基于灾变动力学的神经元系统冲击叠加响应

摘要

With the rapid development of computer science and artificial intelligence technology, the complexity and intelligence of the neural network models constructed by people have been greatly improved. When the complex neuron system is subjected to the impact of "catastrophic", its original characteristics may be changed, and the consequences are difficult to predict. Catastrophe dynamics mainly studies the source of the sudden violent change of nature and human society and its evolution. The impact of the system can be divided into endogenous and exogenous shocks. In this article, catastrophe theory is used to study the neuron system. Based on the mean field model of Hurst and Sornette, introducing the weight parameters, mathematical models are constructed to study the response characteristics of the neuron system in face of exogenous shocks, endogenous shocks, and integrated shocks. The time characteristics of the shock response of the neuron system are discussed too, such as the instantaneous and long-term response of the system in face of shocks, the different response forms according to the weight or linear superposition, and the influence of adjusting parameters on the neuron system. The research result shows that the authoritarian coefficient and weight coefficient have a very important influence on the response of neuron system; By adjusting the two coefficients, the purpose of disaster prevention, self-healing protection and response reducing can be well achieved.%随着计算机科学和人工智能技术的飞速发展,人们构建的神经网络模型的复杂性和智能性得到了极大的提高.当复杂的神经元系统受到"灾变性"的冲击时,其原有特征可能发生变化,后果难以预测.灾变动力学主要研究自然和人类社会突发剧烈变化的根源及其演变.系统所受到的冲击可分为内生冲击和外生冲击.本文在神经元系统通用理论模型的基础上,引入灾变动力学理论展开了研究.基于平均场模型,引入权重系数,建立起数学模型研究神经元系统在面临外生冲击、内生冲击、叠加冲击时的响应特性,并进一步讨论了神经元系统冲击响应的时间特性,如系统面临冲击的瞬时和长期响应,按权重或线性叠加时不同的响应形式,以及调节参数对神经元系统的影响.研究表明,独裁系数和权重系数对神经元系统的响应有着非常重要的影响,对这两个系数进行调整,能很好地实现防灾、自愈保护和减轻灾害的目的.