Center projections for smooth difference equations of mixed type

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:244

Article

Hupkes, H. J.¹  Lunel, S. M. Verduyn¹ 

[1] Leiden Univ, Math Inst, NL-2300 RA Leiden, Netherlands

关键词: mixed type difference equations;    life-cycle model;    center manifold;    Hopf bifurcation;    finite dimensional reduction;    advanced and retarded arguments;    functional differential equations;   

DOI  :  10.1016/j.jde.2007.10.033

来源: Elsevier

【 摘 要 】

We study a class of mixed type difference equations that enjoy a special smoothening property, in the sense that solutions automatically satisfy an associated functional differential equation of mixed type. Using this connection, a finite dimensional center manifold is constructed that captures all solutions that remain sufficiently close to an equilibrium. The results enable a rigorous analysis of a recently developed model in economic theory, that exhibits periodic oscillations in the interest rates of a simple economy of overlapping generations. (C) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free