The purpose of this work is to investigate the properties of spreading speeds for the monotone semiflows. According to the fundamental work of Liang and Zhao [(2007) Comm. Pure Appl. Math.60, 1–40], the spreading speeds of the monotone semiflows can be derived via the principal eigenvalue of linear operators relating to the semiflows. In this paper, we establish a general method to analyse the sign and the continuity of the spreading speeds. Then we consider a limiting case that admits no spreading phenomenon. The results can be applied to the model of cellular neural networks (CNNs). In this model, we find the rule which determines the propagating phenomenon by parameters.

中文翻译：

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单调半流的传播速度分析及其在 CNN 中的应用

这项工作的目的是研究单调半流的传播速度特性。根据梁和赵的基础工作[（2007）通讯。纯应用。数学。60, 1-40]，单调半流的传播速度可以通过与半流相关的线性算子的主特征值导出。在本文中，我们建立了一种分析传播速度的符号和连续性的通用方法。然后我们考虑一个不允许传播现象的极限情况。结果可以应用于细胞神经网络（CNN）的模型。在这个模型中，我们找到了由参数决定传播现象的规律。