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.
出处
《黑龙江大学自然科学学报》
CAS
北大核心
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)
关键词
生物入侵模型
HOPF分支
性别结构
反馈控制
biological invasion model
Hopf bifurcation
sex structure
feedback controls
