Spread rates of spread models with frozen symbols

Ban, Jung-Chao; Hong, Jyy-I; Wu, Yu-Liang (2022-10-17)
 
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URL:
https://doi.org/10.1063/5.0106230

Ban, Jung-Chao
Hong, Jyy-I
Wu, Yu-Liang
American Institute of Physics
17.10.2022

Jung-Chao Ban, Jyy-I Hong, and Yu-Liang Wu, "Spread rates of spread models with frozen symbols", Chaos 32, 103113 (2022) https://doi.org/10.1063/5.0106230

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© AIP publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Jung-Chao Ban, Jyy-I Hong, and Yu-Liang Wu, "Spread rates of spread models with frozen symbols", Chaos 32, 103113 (2022) and may be found at https://doi.org/10.1063/5.0106230.
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doi:https://doi.org/10.1063/5.0106230
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Abstract

This article aims to compare the long-term behavior of a spread model before and after a type in the model becomes frozen, namely, a type of which an individual only produces individuals of the same type. By means of substitution dynamical systems and matrix analysis, the first result of this work gives the spread rates of a 1-spread model with one frozen symbol. Later, in the work, this is shown to hold under more general settings, which include generalized frozen symbols and frozen symbols in \(m\)-spread models. Numerical experiments are provided as supporting evidence for the theory.

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