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Analysis of spreading speeds for monotone semiflows with an application to CNNs

Part of: Representations of solutions General theory in ordinary differential equations Circuits, networks

Published online by Cambridge University Press:  06 March 2019

ZHI-XIAN YU  and
LEI ZHANG Open the ORCID record for LEI ZHANG [Opens in a new window]
ZHI-XIAN YU
Affiliation:
Mathematics and Science, College, Shanghai Normal University, Shanghai200234, P. R. China e-mail: zxyu0902@163.com College of Science, University of Shanghai for Science and TechnologyShanghai200093, China e-mail: zxyu0902@163.com
LEI ZHANG
Affiliation:
Department of Mathematics, Harbin Institute of Technology in Weihai Weihai, Shandong264209, China e-mail: zhanglei890512@gmail.com
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Abstract

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.

Keywords

Spreading speedstravelling wavesmonotone semiflowsCNNs

MSC classification

Primary: 35C07: Traveling wave solutions
Secondary: 34A33: Lattice differential equations 94C99: None of the above, but in this section
Type
Papers
Information
European Journal of Applied Mathematics , Volume 31 , Issue 3 , June 2020 , pp. 369 - 384
Copyright
© Cambridge University Press 2019

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