Coefficient criterion for shil'nikov chaos: Application to a simple investment model

Eiji Tsuzuki; Shunsuke Shinagawa; Tomohiro Inoue

Coefficient criterion for shil'nikov chaos: Application to a simple investment model

Eiji Tsuzuki, Shunsuke Shinagawa, Tomohiro Inoue

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

This chapter (a) represents one of the conditions of the Shil'nikov theorem in terms of the coefficients of a characteristic equation, and (b) demonstrates the existence of chaos by applying the theorem to a simple investment model. To demonstrate the existence of chaos, we adopt a numerical method of combining a condition of the Shil'nikov theorem with Kopell and Howard's theorem. Consistently with our intuition, it is confirmed that the more active the firm's expectations about investment, the more complex the economic behavior.

Original language	English
Title of host publication	Business Cycles in Economics: Types, Challenges and Impacts on Monetary Policies
Publisher	Nova Science Publishers, Inc.
Pages	69-86
Number of pages	18
ISBN (Print)	9781633215382, 9781633213227
Publication status	Published - 2014 Jul 1

Keywords

Adjustment costs of investment
Chaos
Homoclinic orbit
Hopf bifurcation
Period doubling bifurcation

ASJC Scopus subject areas

Business, Management and Accounting(all)

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N2 - This chapter (a) represents one of the conditions of the Shil'nikov theorem in terms of the coefficients of a characteristic equation, and (b) demonstrates the existence of chaos by applying the theorem to a simple investment model. To demonstrate the existence of chaos, we adopt a numerical method of combining a condition of the Shil'nikov theorem with Kopell and Howard's theorem. Consistently with our intuition, it is confirmed that the more active the firm's expectations about investment, the more complex the economic behavior.

AB - This chapter (a) represents one of the conditions of the Shil'nikov theorem in terms of the coefficients of a characteristic equation, and (b) demonstrates the existence of chaos by applying the theorem to a simple investment model. To demonstrate the existence of chaos, we adopt a numerical method of combining a condition of the Shil'nikov theorem with Kopell and Howard's theorem. Consistently with our intuition, it is confirmed that the more active the firm's expectations about investment, the more complex the economic behavior.

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