# American Institute of Mathematical Sciences

March  2018, 7(1): 79-93. doi: 10.3934/eect.2018005

## Stability problem for the age-dependent predator-prey model

 1 Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Łojasiewicza 6, 30-348 Kraków, Poland 2 Faculty of Computer Science, Bialystok University of Technology, ul. Wiejska 45A, 15-351 Białystok, Poland

* Corresponding author: Anna Poskrobko, a.poskrobko@pb.edu.pl.

Received  December 2016 Revised  July 2017 Published  January 2018

Fund Project: The contribution of Anna Poskrobko was supported by the Bialystok University of Technology grant S/WI/1/2016 and founded by the resources for research by Ministry of Science and Higher Education.

The paper deals with the age-dependent model which is a generalization of the classical Lotka-Volterra model. Age structure of both species, predators and preys is concerned. The model is based on the system of partial differential and integro-differential equations. We study the existence and uniqueness of the solution for the considered population problem. The stability problem for trivial stationary solution of the model is also proved.

Citation: Antoni Leon Dawidowicz, Anna Poskrobko. Stability problem for the age-dependent predator-prey model. Evolution Equations & Control Theory, 2018, 7 (1) : 79-93. doi: 10.3934/eect.2018005
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