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European Journal of Applied Mathematics (1)

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1 results

Analysis of spreading speeds for monotone semiflows with an application to CNNs
Part of
ZHI-XIAN YU, LEI ZHANG
Journal:

European Journal of Applied Mathematics / Volume 31 / Issue 3 / June 2020

Published online by Cambridge University Press:

06 March 2019, pp. 369-384
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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.