Non-constant positive solutions of a general Gause-type predator-prey system with self- and cross-diffusions

Pan Xue¹ ; Yunfeng Jia² ; Cuiping Ren¹ ; Xingjun Li¹

¹ School of General Education, Xi’an Eurasia University, Xi’an, Shaanxi 710065, China.
² School of Mathematics and Statistics, Shaanxi Normal University, Xi’an, Shaanxi 710062, China.

Mathematical modelling of natural phenomena, Tome 16 (2021), article no. 25

Résumé

In this paper, we investigate the non-constant stationary solutions of a general Gause-type predator-prey system with self- and cross-diffusions subject to the homogeneous Neumann boundary condition. In the system, the cross-diffusions are introduced in such a way that the prey runs away from the predator, while the predator moves away from a large group of preys. Firstly, we establish a priori estimate for the positive solutions. Secondly, we study the non-existence results of non-constant positive solutions. Finally, we consider the existence of non-constant positive solutions and discuss the Turing instability of the positive constant solution.

Détail

DOI : 10.1051/mmnp/2021017

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