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Zbl 1243.34116
Faria, Teresa
Global asymptotic behaviour for a Nicholson model with patch structure and multiple delays. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 18, 7033-7046 (2011). ISSN 0362-546X

The author considers a Nicholson's blowflies model on a patch environment allowing different maturation delay in different patches. The main concern is the global dynamics of the model system. Conditions for the absolute global asymptotic stability of both the trivial equilibrium and a positive equilibrium (when it exists) are given. The existence of positive heteroclinic solutions connecting the two equilibria is also addressed. The author also further studies a diffusive Nicholson-type model with patch structure, and establishes a criterion for the existence of positive travelling wave solutions, for large wave speeds. Several applications illustrate the results, improving some criteria in the recent literature.
[Xingfu Zou (London, Ontario)]

MSC 2000:: *34K60 Applications of functional-differential equations
34K20 Stability theory of functional-differential equations
34K25 Asymptotic theory of functional-differential equations
92D25 Population dynamics
35C07

Keywords: Nicholson's blowflies equation; delays; patch structure; global asymptotic stability; heteroclinic solution; travelling wave

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