Geometric Analysis of Ecological Models with Slow and Fast Processes

被引：0

作者：

Sergio Rinaldi

Marten Scheffer

机构：

[1] CIRITA,

[2] Politecnico di Milano,undefined

[3] Via Ponzio 34/5,undefined

[4] 20133 Milano,undefined

[5] Italy,undefined

[6] Department of Aquatic Ecology and Water Quality Management,undefined

[7] Agricultural University Wageningen,undefined

[8] P.O. Box 8080,undefined

[9] NL-6700 DD Wageningen,undefined

[10] The Netherlands,undefined

来源：

Ecosystems | 2000年 / 3卷

关键词：

slow-fast dynamics; singular perturbation; catastrophes; bifurcation analysis; quasi-steady state; slow-fast cycles.;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

The interaction of fast and slow processes is an integral part of the sudden large shifts that sometimes occur in ecosystems. To study the effects of slow/fast variables on ecosystems, we used a range of examples from natural and exploited aquatic and terrestrial systems. So-called catastrophic bifurcations in the dynamics of the fast components are at the heart of such dramatic shifts. We discuss some of the most important bifurcations and show how they can be analyzed. Subsequently, we show how the interaction with slowly changing variables can be understood from graphs constructed in a simple way using the singular perturbation approach.

引用

页码：507 / 521

页数：14