Akhmet Marat, Tleubergenova Madina, Zhamanshin Akylbek
Department of Mathematics, Middle East Technical University, Ankara 06531, Turkey.
Department of Mathematics, Aktobe Regional University, Aktobe 030000, Kazakhstan.
Entropy (Basel). 2022 Oct 29;24(11):1555. doi: 10.3390/e24111555.
In this paper, we rigorously prove that unpredictable oscillations take place in the dynamics of Hopfield-type neural networks (HNNs) when synaptic connections, rates and external inputs are modulo periodic unpredictable. The synaptic connections, rates and inputs are synchronized to obtain the convergence of outputs on the compact subsets of the real axis. The existence, uniqueness, and exponential stability of such motions are discussed. The method of included intervals and the contraction mapping principle are applied to attain the theoretical results. In addition to the analysis, we have provided strong simulation arguments, considering that all the assumed conditions are satisfied. It is shown how a new parameter, degree of periodicity, affects the dynamics of the neural network.
在本文中，我们严格证明，当突触连接、速率和外部输入是模周期不可预测时，霍普菲尔德型神经网络（HNNs）的动力学中会发生不可预测的振荡。对突触连接、速率和输入进行同步，以获得实轴紧子集上输出的收敛性。讨论了此类运动的存在性、唯一性和指数稳定性。应用包含区间法和压缩映射原理来获得理论结果。除了分析之外，考虑到所有假设条件均得到满足，我们还提供了有力的仿真论证。展示了一个新参数——周期性程度——如何影响神经网络的动力学。
