TRAVELING PULSES AND THEIR BIFURCATION IN A DIFFUSIVE ROSENZWEIG-MACARTHUR SYSTEM WITH A SMALL PARAMETER

被引：0

作者：

Hou, X. I. A. O. J. I. E. ^{[1
]}

LI, Y. I. ^{[2
]}

机构：

[1] Univ North Carolina Wilmington, Dept Math & Stat, Wilmington, NC 28403 USA

[2] City Univ New York, John Jay Coll Criminal Justice, Dept Math & Comp Sci, New York, NY 10019 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2022年

关键词：

Traveling pulses; homoclinic orbits; geometric singular perturbations; transversality; Melnikov?s function; Exchange Lemma; HOMOCLINIC BIFURCATIONS; STABILITY; ORBITS; WAVES; EXISTENCE;

D O I：

10.3934/dcdsb.2022186

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Conditions for the long term coexistence of the prey and preda -tor populations of a diffusive Rosenzweig-MacArthur model are studied. The coexistence is represented by traveling pulses, which approach a coexistence equilibrium state as the moving coordinate approaches to infinities. Three dif-ferent pulses, according to their speeds, are analyzed by regular perturbation as well as geometric singular perturbation methods. We further show that the pulses are connected by a bifurcation curve (surface) in parametric space. The paper concludes with several numerical simulations.

引用

页码：2655 / 2680

页数：26