کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
966921 | 931122 | 2010 | 21 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Chaotic sets and Euler equation branching
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
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چکیده انگلیسی
Some macroeconomic models may exhibit a type of indeterminacy known as Euler equation branching (e.g., the one-sector growth model with a production externality). The dynamics in such models are governed by a differential inclusion xËâH(x), where H is a set-valued function. In this paper, we introduce the concept of a chaotic set and explore its implications for Devaney chaos, Li-Yorke chaos and distributional chaos (adapted to dynamical systems generated by a differential inclusion). We show that a chaotic set will imply Devaney and Li-Yorke chaos and that a chaotic set with Euler equation branching will imply distributional chaos. We show that the existence of a steady state for a differential inclusion on the plane will generate a chaotic set and hence Devaney and Li-Yorke chaos. As an application, we show how these results can be applied to a one-sector growth model with a production externality - extending the results of Christiano and Harrison (1999). We show that chaotic (Devaney, Li-Yorke and distributional) and cyclic equilibria are possible and that this behavior is not dependent on the steady state being “locally” a saddle, sink or source.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Economics - Volume 46, Issue 6, 20 November 2010, Pages 1173-1193
Journal: Journal of Mathematical Economics - Volume 46, Issue 6, 20 November 2010, Pages 1173-1193
نویسندگان
Brian E. Raines, David R. Stockman,