Accurate Approximation of Homoclinic Solutions in Gray-Scott Kinetic Model

被引：10

作者：

Kuznetsov, Yu. A. ^{[1
]}

Meijer, H. G. E. ^{[1
]}

Al-Hdaibat, B. ^{[2
]}

Govaerts, W. ^{[2
]}

机构：

[1] Univ Twente, Dept Appl Math, NL-7500 AE Enschede, Netherlands

[2] Univ Ghent, Dept Appl Math & Comp Sci, B-9000 Ghent, Belgium

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2015年 / 25卷 / 09期

关键词：

Gray-Scott model; Bogdanov-Takens bifurcation; homoclinic orbit; MatCont; BIFURCATION-ANALYSIS; OSCILLATIONS; MATCONT;

D O I：

10.1142/S0218127415501254

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The second-order predictor for the homoclinic orbit is applied to the Gray-Scott model. The problem is used to illustrate the approximation of the homoclinic orbits near a generic Bogdanov-Takens bifurcation in n-dimensional systems of differential equations. In the process, we show that it is necessary to take (usually ignored) cubic terms in the Bogdanov-Takens normal form into account to derive a correct second-order prediction for the homoclinic bifurcation curve. The analytic solutions are compared with those obtained by numerical continuation.

引用

页数：10

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