Bifurcation Near a Transcritical Singularity in Planar Singularly Perturbed Systems

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics Pub Date : 2024-11-10 DOI:10.1111/sapm.12787

Jianhe Shen, Xiang Zhang, Kun Zhu

引用次数: 0

Abstract

We classify all bifurcation phenomena of the flow near a transcritical singularity in planar singularly perturbed differential systems that do not have a breaking parameter via qualitative analysis and blow-up technique. Here, the directional blown up vector fields can have several singularities and no first integral that are different from those in the literatures. The obtained local bifurcations are also illustrated by numerical simulations through a modified Leslie–Gower model, whose global dynamics is thereby obtained.

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平面奇异扰动系统跨临界奇点附近的分岔

我们通过定性分析和吹胀技术，对不存在断裂参数的平面奇异扰动微分系统中跨临界奇点附近流动的所有分岔现象进行了分类。在这里，定向吹大的矢量场可能有多个奇点，并且没有第一积分，这与文献中的奇点不同。我们还通过数值模拟来说明所得到的局部分岔，并由此得到了一个修正的莱斯利-高尔模型的全局动力学。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Studies in Applied Mathematics 数学-应用数学

CiteScore

4.30

自引率

3.70%

发文量

审稿时长

>12 weeks

期刊介绍： Studies in Applied Mathematics explores the interplay between mathematics and the applied disciplines. It publishes papers that advance the understanding of physical processes, or develop new mathematical techniques applicable to physical and real-world problems. Its main themes include (but are not limited to) nonlinear phenomena, mathematical modeling, integrable systems, asymptotic analysis, inverse problems, numerical analysis, dynamical systems, scientific computing and applications to areas such as fluid mechanics, mathematical biology, and optics.