期刊文献+

Positive solutions for a Lotka-Volterra prey-predator model with cross-diffusion and Holling type-Ⅱ functional response 被引量:5

Positive solutions for a Lotka-Volterra prey-predator model with cross-diffusion and Holling type-Ⅱ functional response
原文传递
导出
摘要 We consider a Lotka-Volterra prey-predator model with cross-diffusion and Holling type-II functional response.The main concern is the existence of positive solutions under the combined effect of cross-diffusion and Holling type-II functional response.Here,a positive solution corresponds to a coexistence state of the model.Firstly,we study the sufficient conditions to ensure the existence of positive solutions by using degree theory and analyze the coexistence region in parameter plane.In addition,we present the uniqueness of positive solutions in one dimension case.Secondly,we study the stability of the trivial and semi-trivial solutions by analyzing the principal eigenvalue of the corresponding linearized system,and then we characterize the stable/unstable regions of semi-trivial solutions in parameter plane. We consider a Lotka-Volterra prey-predator model with cross-diffusion and Holling type-II functional response. The main concern is the existence of positive solutions under the combined effect of cross-diffusion and Holling type-II functional response. Here,a positive solution corresponds to a coexistence state of the model. Firstly,we study the sufficient conditions to ensure the existence of positive solutions by using degree theory and analyze the coexistence region in parameter plane. In addition,we present the uniqueness of positive solutions in one dimension case. Secondly,we study the stability of the trivial and semi-trivial solutions by analyzing the principal eigenvalue of the corresponding linearized system,and then we characterize the stable/unstable regions of semi-trivial solutions in parameter plane.
出处 《Science China Mathematics》 SCIE 2014年第5期991-1010,共20页 中国科学:数学(英文版)
基金 supported by National Natural Science Foundation of China(Grant No.11201380) the Fundamental Research Funds for the Central Universities(Grant No.XDJK2012B007) Doctor Fund of Southwest University(Grant No.SWU111021) Educational Fund of Southwest University(Grant No.2010JY053) National Research Foundation of Korea Grant funded by the Korean Government(Ministry of Education,Science and Technology)(Grant No.NRF-2011-357-C00006)
关键词 HollingⅡ型功能性反应 VOLTERRA型 正解的存在性 交叉扩散 捕食模型 HollingⅡ类功能反应 g型 参数平面 Lotka-Volterra prey-predator model Holling type-II functional response cross-diffusion positive solutions coexistence uniqueness degree theory
  • 相关文献

参考文献1

二级参考文献1

共引文献7

同被引文献13

引证文献5

二级引证文献9

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部