Dynamics of the logistic delay equation with a large spatially distributed control coefficient

被引：0

作者：

I. S. Kashchenko

S. A. Kashchenko

机构：

[1] Yaroslavl State University,

[2] National Research Nuclear University “MEPhI,undefined

[3] ”,undefined

来源：

Computational Mathematics and Mathematical Physics | 2014年 / 54卷

关键词：

dynamics of the logistic delay equation; spatially distributed control; bifurcation; asymptotic methods; parabolic equations;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

The local dynamics of the logistic delay equation with a large spatially distributed control coefficient is asymptotically studied. The basic bifurcation scenarios are analyzed depending on the relations between the parameters of the equation. It is shown that the equilibrium states can lose stability even for asymptotically small values of the delay parameter. The corresponding critical cases can have an infinite dimension. Special nonlinear parabolic equations are constructed whose nonlocal dynamics determine the local behavior of solutions to the original boundary value problem.

引用

页码：785 / 796

页数：11

共 10 条

[1]

Kashchenko S A(2012)Asymptotics of solutions of the generalized Hutchinson equation Model. Anal. Inf. Sist. 19 32-62

[2]

Kashchenko S A(1987)On steady states of the Hutchinson equation with diffusion Dokl. Akad. Nauk SSSR 292 327-330

[3]

Kuramoto Y(2002)Coexisting of coherence and incoherence in nonlocally coupled phase oscillators Nonlin. Phenom. Complex Syst. 5 380-385

[4]

Battogtokh D(2011)Dynamics of an equation with a large spatially distributed control parameter Dokl. Math. 83 408-412

[5]

Kashchenko I S(1988)On quasi-normal forms for parabolic systems with weak diffusion Dokl. Akad. Nauk SSSR 299 1049-1053

[6]

Kashchenko S A(1996)Normalization in the systems with small diffusion Int. J. Bifurcations Chaos 6 1093-1109

[7]

Kashchenko S A(2010)Multistability in nonlinear parabolic systems with low diffusion Dokl. Math. 82 878-881

[8]

Kaschenko S A(1998)The Ginzburg-Landau equation as a normal form for a second-order difference-differential equation with a large delay Comput. Math. Math. Phys. 38 443-451

[9]

Kashchenko I S(undefined)undefined undefined undefined undefined-undefined

[10]

Kashchenko S A(undefined)undefined undefined undefined undefined-undefined

← 1 →