Ivlev型捕食系统的全局动力学分析

基金项目: 宁波市自然科学基金资助项目(2006A610032)

Global Analysis of Ivlev’s Type Predator-Prey Dynamical System

Department of Mathematics, Ningbo University, Ningbo, Zhejiang 315211, P. R. China;

摘要: 研究捕食者与食饵均具有线性密度制约的Ivlev型捕食动力系统．应用常微分方程定性方法,得到了正平衡点的全局稳定性和非小振幅极限环的存在唯一性的充分条件．特别地,在一定条件下,证明了极限环的存在唯一性与正平衡点的局部不稳定性是等价的，正平衡点的局部稳定性隐含它的全局稳定性，因此，系统的全局动力学性质完全由正平衡点的局部性质所决定．
- 极限环 /
- 全局稳定性 /
- 密度制约 /
- Ivlev功能反应 /
- 存在唯一性
Abstract: A class of Ivlev. s type predator-prey dynamic systems with prey and predator both having linear density restricts is considered. By using the qualitative methods of ODE, the positive equilibrium's global stability and existence and uniqueness of non-small amplitude stable limit cycle were obtained. Especially under certain conditions, it shows that existence and uniqueness of non-small amplitude stable limit cycle is equivalent to the positive equilibrium's local unstability and the positive equilibrium's local stability implies its global stability. That is to say, the global dynamic of the system is entirely determined by the local stability of the positive equilibrium.
- limit cycle /
- global stability /
- density restrict /
- Ivlev type functional response /
- existence and uniqueness

[1]	Sugie Jitsuro.Two-parameter bifurcation in a predator-prey system of Ivelv type[J].Journal of Mathematical Analysis and Application，1998,217(2):349-371. doi: 10.1006/jmaa.1997.5700
[2]	Kooij R E,Zegeling Z.A predator-prey model with Ivlev's functional response[J].Journal of Mathematical Analysis and Application,1996,198(2):473-489.[JP3]. De Angelis D L,Goldstein R A,O'Neill R V.A model for tropic interaction[J].Ecology,1975(56):881-892. doi: 10.1006/jmaa.1996.0093
[4]	唐秋林.一类具Ivlev型功能反应的捕食者食饵系统[J].北华大学学报(自然科学版),2002,3(5):381-384.
[5]	FENG Jian-wen,CHEN Shi-hua.Global asympotic behavior for the competing predators of the Ivlev types[J].Mathematica Applicata,2000,13(4):85-88.