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Global asymptotic behaviour for a Nicholson model with patch structure and multiple delays. (English) Zbl 1243.34116
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.

##### MSC:
 34K60 Qualitative investigation and simulation of models involving functional-differential equations 34K20 Stability theory of functional-differential equations 34K25 Asymptotic theory of functional-differential equations 92D25 Population dynamics (general) 35C07 Traveling wave solutions
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