The parameter functionalization method for the problem of saddle-node bifurcations in dynamical systems

被引：0

作者：

M. G. Yumagulov

E. S. Imangulova

机构：

[1] Bashkiria State University,

来源：

Automation and Remote Control | 2017年 / 78卷

关键词：

dynamical system; saddle-node bifurcation; periodic oscillations; synchronization; stability; parameter functionalization;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We propose new sufficient conditions for saddle-node bifurcations in one- and twoparametric dynamical systems obtained with the parameter functionalization method, derive asymptotic formulas for the resulting solutions, and analyze their stability. As an application, we consider the synchronization problem for periodic oscillations of an autonomous Van der Pol generator under an external harmonic influence.

引用

页码：630 / 642

页数：12

共 7 条

[1]

Kozyakin V.S.(1980)Method of Parameter Functionalization in the Problem of Bifurcation Points Dokl. Akad. Nauk SSSR 254 1061-1064

[2]

Krasnosel’skii M.A.(2007)Parameter Functionalization and Its Application to the Problem of Local Bifurcations in Dynamic Systems Autom. Remote Control 68 573-582

[3]

Ibragimova L.S.(2010)The Operator Method for Approximate Study of Proper Bifurcation in Multiparametric Dynamical Systems Ufim. Mat. Zh. 2 3-26

[4]

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