# American Institute of Mathematical Sciences

August  2013, 18(6): 1567-1579. doi: 10.3934/dcdsb.2013.18.1567

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

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

Received  September 2011 Revised  January 2012 Published  March 2013

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.
Citation: Teresa Faria. Asymptotic behaviour for a class of delayed cooperative models with patch structure. Discrete & Continuous Dynamical Systems - B, 2013, 18 (6) : 1567-1579. doi: 10.3934/dcdsb.2013.18.1567
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