## 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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### References:

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