Travelling waves in the Holling-Tanner model with weak diffusion

被引：26

作者：

Ghazaryan, Anna ^{[1
]}

Manukian, Vahagn ^{[2
]}

Schecter, Stephen ^{[3
]}

机构：

[1] Miami Univ, Dept Math, Oxford, OH 45056 USA

[2] Miami Univ, Dept Math, Hamilton, OH 45011 USA

[3] N Carolina State Univ, Dept Math, Raleigh, NC 27695 USA

来源：

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2015年 / 471卷 / 2177期

基金：

美国国家科学基金会;

关键词：

geometric singular perturbation theory; travelling front; periodic wave train; predator-prey model; diffusive Holling-Tanner model; entry-exit function; SINGULAR PERTURBATION-THEORY; PREDATOR-PREY MODEL;

D O I：

10.1098/rspa.2015.0045

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

For a wide range of parameters, we study travelling waves in a diffusive version of the Holling-Tanner predator-prey model from population dynamics. Fronts are constructed using geometric singular perturbation theory and the theory of rotated vector fields. We focus on the appearance of the fronts in various singular limits. In addition, periodic travelling waves of relaxation oscillation type are constructed using a recent generalization of the entry-exit function.

引用

页数：16

共 23 条

[1]

[Anonymous], 2013, Mathematical Biology

[2]

[Anonymous], 2015, Multiple time scale dynamics

[3] Turing instabilities and spatio-temporal chaos in ratio-dependent Holling-Tanner model [J].