Math. Model. Nat. Phenom.
Volume 16, 2021
Reviews in mathematical modelling
|Number of page(s)||15|
|Published online||21 April 2021|
Non-constant positive solutions of a general Gause-type predator-prey system with self- and cross-diffusions*
School of General Education, Xi’an Eurasia University, Xi’an,
2 School of Mathematics and Statistics, Shaanxi Normal University, Xi’an, Shaanxi 710062, China.
** Corresponding author: email@example.com
Accepted: 22 March 2021
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.
Mathematics Subject Classification: 35K51 / 35K57 / 35A01 / 35A09
Key words: Cross-diffusion / predator-prey system / positive solutions / Leray-Schauder degree / stability
© The authors. Published by EDP Sciences, 2021
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