Existence and stability of a spike in the central component for a consumer chain model in a two-dimensional domain
In this paper, we study a three-component consumer chain model which is based on Schnakenberg type kinetics in a two-dimensional domain. In the model there is one consumer feeding on the producer and a second consumer feeding on the first consumer. Through a rigorous analysis, we show that there exi...
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Published in | Nonlinear analysis Vol. 221; p. 112880 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Elsevier Ltd
01.08.2022
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Subjects | |
Online Access | Get full text |
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Summary: | In this paper, we study a three-component consumer chain model which is based on Schnakenberg type kinetics in a two-dimensional domain. In the model there is one consumer feeding on the producer and a second consumer feeding on the first consumer. Through a rigorous analysis, we show that there exist two different single spike solutions if the feed rates are small. Further, we also establish the stability results: If the time-relaxation constants for both producer and the second consumer vanish, the large amplitude spike solution is stable and the small-amplitude spike solution is unstable. We also derive results on the stability of solutions when these two time-relaxation constants are positive. We show a new effect that if the time-relaxation constant of the second consumer is bounded, the large-amplitude spike solution is still stable while it is unstable in the one-dimensional case. |
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ISSN: | 0362-546X 1873-5215 |
DOI: | 10.1016/j.na.2022.112880 |