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

IF 2.6 4区数学 Q2 MATHEMATICAL & COMPUTATIONAL BIOLOGY

Mathematical Modelling of Natural Phenomena Pub Date : 2021-03-26 DOI:10.1051/MMNP/2021017

Pan Xue, Yunfeng Jia, Cuiping Ren, Xingjun Li

引用次数: 4

Abstract

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.

查看原文本刊更多论文

具有自扩散和交叉扩散的一般Gause型捕食-被捕食系统的非常正解

本文研究了一类具有自扩散和交叉扩散的一般高斯型捕食-食饵系统在齐次Neumann边界条件下的非常平稳解。在这个系统中，交叉扩散是以这样一种方式引入的:猎物从捕食者那里逃跑，而捕食者也从一大群猎物那里逃走。首先，我们建立了正解的先验估计。其次，研究了非常正解的不存在性结果。最后，我们考虑了非常正解的存在性，并讨论了正常解的图灵不稳定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Mathematical Modelling of Natural Phenomena MATHEMATICAL & COMPUTATIONAL BIOLOGY-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

5.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Mathematical Modelling of Natural Phenomena (MMNP) is an international research journal, which publishes top-level original and review papers, short communications and proceedings on mathematical modelling in biology, medicine, chemistry, physics, and other areas. The scope of the journal is devoted to mathematical modelling with sufficiently advanced model, and the works studying mainly the existence and stability of stationary points of ODE systems are not considered. The scope of the journal also includes applied mathematics and mathematical analysis in the context of its applications to the real world problems. The journal is essentially functioning on the basis of topical issues representing active areas of research. Each topical issue has its own editorial board. The authors are invited to submit papers to the announced issues or to suggest new issues. Journal publishes research articles and reviews within the whole field of mathematical modelling, and it will continue to provide information on the latest trends and developments in this ever-expanding subject.