摘要
探讨了一类具有时滞和非线性Michaelis-Menten型收获的捕食系统.利用微分方程的稳定性理论和Hopf分支理论,研究模型的动力学行为.分析了系统存在唯一正平衡点的条件,系统正平衡点渐近稳定的条件,并且给出了滞量作为参数时存在临界值使系统在一定范围内正平衡点仍保持稳定,而在其等于临界滞量时系统在正平衡点处出现Hopf分支的结论.
In this paper, a predator-prey system with time delay and nonlinear Michaelis-Menten type harvesting is discussed. By using qualitative theory, stability theory and Hopf bifurcation theory of differential equation, the author studies the dynamic behavior of the model. The author analyzes the conditions to guarantee existence and uniqueness of the positive equilibrium and to make the positive equilibrium asymptotic stability for the system. The author derives the critical value of delay to still guarantee the positive equilibrium of system stable in the cer- tain range but to exhibit Hopf bifurcation as the delay pass through it, when the delay is viewed as bifurcation pa- rameter.
作者
胡志东
HU Zhi-dong(School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Chin)
出处
《南阳师范学院学报》
CAS
2017年第3期12-15,共4页
Journal of Nanyang Normal University
