非线性扩散和非线性出生率对两斑块生态模型的影响  

Effects of nonlinear diffusion and nonlinear birth rate on the two-patch model

作　　者：夏越 陈丽娟[1] XIA Yue;CHEN Li-juan(School of Mathematics and Statistics,Fuzhou University,Fuzhou,Fujian 350108,China)

机构地区：[1]福州大学数学与统计学院,福建福州350108

出　　处：《宁德师范学院学报（自然科学版）》2024年第3期225-234,300,共11页Journal of Ningde Normal University(Natural Science)

基　　金：福建省自然科学基金资助项目(2021J01614)。

摘　　要：研究一类单种群斑块模型,其中斑块间的扩散是非线性的,并且斑块1的种群出生率依赖于自身的种群密度,当依赖系数β越大,出生率就越小.详细分析所有可能的平衡点的局部稳定性以及全局稳定性,并且通过证明横截性条件发现,系统可能发生跨临界分支.结果还表明,非线性扩散可以显著降低斑块1的种群灭绝的风险,并且当β处于一定范围时,非线性扩散有利于种群密度的增长.A single-population plaque model is presented in which the diffusion between plaques is nonlinear and the birth rate of the first patch depends on its population density,and the higher the dependency coefficientβ,the smaller the birth rate.The local stability of all possible equilibrium points and the global stability condition are proved.By proving the transverse condition,the system may undergo critical branches.The results also indicate that,the nonlinear diffusion significantly reduces the risk of population extinction in the first patch and is associated with population density growth whenβis in a certain range.

关 键 词：非线性出生率 非线性扩散 稳定性 跨临界分支 

分 类 号：O141[理学—数学]