Asymptotic behaviour for a class of delayed cooperative models with patch structure

Teresa Faria

doi:10.3934/dcdsb.2013.18.1567

Article Contents

2013, Volume 18, Issue 6: 1567-1579. Doi: 10.3934/dcdsb.2013.18.1567

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Asymptotic behaviour for a class of delayed cooperative models with patch structure

Teresa Faria^1,

1.
Departamento de Matemática and CMAF, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa

Received: August 31, 2011

Revised: December 31, 2011

Published: July 2013

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Abstract

For a class of cooperative population models with patch structure and multiple discrete delays, we give conditions for the absolute global asymptotic stability of both the trivial solution and -- when it exists -- a positive equilibrium. Under a sublinearity condition, sharper results are obtained. The existence of positive heteroclinic solutions connecting the two equilibria is also addressed. As a by-product, we obtain a criterion for the existence of positive traveling wave solutions for an associated reaction-diffusion model with patch structure. Our results improve and generalize criteria in the recent literature.

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Mathematics Subject Classification: Primary: 34K20; Secondary: 34K25, 35C07, 92D25.

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References

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