DYNAMICS OF MODIFIED PREDATOR-PREY MODELS

被引：6

作者：

Kloeden, P. E. ^{[1
]}

Poetzsche, C. ^{[2
]}

机构：

[1] Goethe Univ Frankfurt, Inst Math, D-60054 Frankfurt, Germany

[2] Tech Univ Munich, Zentrum Math, D-85758 Garching, Germany

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2010年 / 20卷 / 09期

关键词：

Predator-prey models; Lotka-Volterra equations; principle of mass action; atto-fox problem; linearly modified Lotka-Volterra equations; Poincare map; nonsmooth dynamical system; global attractor; repeller; STABILITY; SYSTEM;

D O I：

10.1142/S0218127410027271

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Besides being structurally unstable, the Lotka-Volterra predator-prey model has another shortcoming due to the invalidity of the principle of mass action when the populations are very small. This leads to extremely large populations recovering from unrealistically small ones. The effects of linear modifications to structurally unstable continuous-time predator-prey models in a (small) neighbourhood of the origin are investigated here. In particular, it is shown that typically either a global attractor or repeller arises depending on the choice of coefficients. The analysis is based on Poincare mappings, which allow an explicit representation for the classical Lotka-Volterra equations.

引用

页码：2657 / 2669

页数：13

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