Canard cycles for predator–prey systems with Holling types of functional response☆

By Chengzhi Li, Huaiping Zhu. 2013

118 citations recorded by the source corpus.

Abstract By using the singular perturbation theory developed by Dumortier and Roussarie and recent work of De Maesschalck and Dumortier, we study the canard phenomenon for predator–prey systems with response functions of Holling types. We first develop a formula for computing the slow divergence integrals. By using the formula we prove that for the systems with the response function of Holling types III and IV the cyclicity of any limit periodic set is at most two, that is at most two families of hyperbolic limit cycles or at most one family of limit cycles with multiplicity two can bifurcate from the limit periodic set by small perturbations. We also indicate the regions in parameter space where the corresponding limit periodic set has cyclicity at most one or at most two.

Subfields: Computer Networks and Communications, Geometry and Topology, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/03cd59f17aa92bdeaf694b307a6f06b8baf39b13

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In Computer Networks and Communications

1. Jicai Huang
2. Shigui Ruan
3. Wan-Tong Li
4. Junjie Wei
5. Yong-Hong Fan

In Geometry and Topology

1. Shigui Ruan
2. Jicai Huang
3. Jinge Song

In Public Health, Environmental and Occupational Health

1. Jicai Huang
2. Shigui Ruan
3. Jinge Song
4. Wan-Tong Li
5. Junjie Wei
6. Guo Lin
7. Yong-Hong Fan

Citations in the corpus

• Bifurcations in a predator–prey system of Leslie type with generalized Holling type III functional response☆ (2014, background): “1.1 in Zhu, Campbell and Wolkowicz [45]).”