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Impulsive diffusion in single species model. (English) Zbl 1131.92071

Summary: In most population models, diffusion between patches is assumed to be continuous or discrete, but in practice many species diffuse only during a single period. We propose a single species model with impulsive diffusion between two patches, which provides a more natural description of population dynamics. By using the discrete dynamical system generated by a monotone, concave map for the population, and \(\varepsilon _{1} - \varepsilon _{2}\) variation, we prove that the map always has a globally stable positive fixed point. This means that a single species system with impulsive diffusion always has a globally stable positive periodic solution. This result is further substantiated by numerical simulations.

MSC:

92D40 Ecology
37N25 Dynamical systems in biology
39A11 Stability of difference equations (MSC2000)
39A12 Discrete version of topics in analysis
92D25 Population dynamics (general)
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