摘要
文章讨论了一类边界条件为Neumann边界、带有饱和与竞争项的捕食模型,获得了模型非负常稳态解的存在性和渐近行为的充分条件,即在条件0<k<a/(1+ab)和a≥1/c下,模型存在唯一的非负常稳态解,并且当kb(c+kb2-b)>ac2时,此非负常稳态解是渐近稳定的。由于模型不具有单调性或混拟单调性,因此传统的上下解方法不能直接使用,为此改进了上下解和迭代方法,并结合抛物方程比较原理获得非负常稳态解的渐近行为,此结果表明扩散不影响非负常稳态解的渐近行为。
In this paper, a predator-prey model with predator saturation and competition function response under homogeneous Neumann boundary condition is considered. The sufficient conditions of existence of the nonnegative constant steady states solutions： 0〈k〈a/（1＋ab） ,a≥l/c are obtained, and some sufficient conditions：kb（c＋kb^2 -b）〉ac^2 to guarantee the asymptotic behavior of the nonnegative constant steady states solutions are given. Since the model which we study hasn＇t monotonieity or mixed quasi monotonicity, so the traditional upper-lower solutions and iteration methods suit the model. To this end, we improve the upper-lower solutions and iteration method, and integrate with the parabolic equation comparison principle, obtain the asymptotic behavior of the nonnegative constant steady states solutions. The result indicates that the asymptotic behavior of the nonnegative constant steady states solutions is independent of the effect of diffusion.
出处
《重庆师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2015年第1期76-80,共5页
Journal of Chongqing Normal University:Natural Science
基金
湖北省教育厅项目(No.Q20122504
No.D20122501)
关键词
捕食模型
比较原理
渐近行为
上下解
predator prey model
comparison principle
asymptotic behavior
upper-lower solutions
