一类具性别结构及反馈控制的生物入侵模型的稳定性及Hopf分支(英文)  

Stability and Hopf bifurcation for a biological invasion model with sex structure and feedback control

作　　者：魏凤英[1] 吴兰琦 

机构地区：[1]福州大学数学与计算机科学学院,福州350116

出　　处：《黑龙江大学自然科学学报》2014年第6期710-718,共9页Journal of Natural Science of Heilongjiang University

基　　金：Supported by the National Natural Science Foundation of China(11201075);the Natural Science Foundation of Fujian Province(2010J01005)

摘　　要：研究一类具性别结构及反馈控制生物入侵模型的稳定性及Hopf分支。利用Hopf分支定理,得到正平衡点处发生Hopf的充分条件;运用规范型方法和中心流形定理,得到分支方向及分支周期解。分析雄性食饵种群与雌性食饵种群的性别比例变化,及反馈控制对正平衡点的影响,数值模拟说明所得结论的有效性。Stability and Hopf bifurcation for a biological invasion model with sex structure and feedback control are investigated. By the Hopf bifurcation theorem, the sufficient conditions of Hopf bifurca- tion occurring at the positive equilibrium are obtained. Moreover, by means of the normal form method and center manifold theorem, the direction of Hopf bifurcation and bifurcated periodic solutions are deduced. Then, the change rate of sex ratio for the male prey and the female prey is analyzed, and the influence of feedback control for the positive equilibrium is discussed. Finally, the numerical simulations are carried out to illustrate our main results.

关 键 词：生物入侵模型 HOPF分支 性别结构 反馈控制 

分 类 号：O175.14[理学—数学]