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

Eiji Tsuzuki*, Shunsuke Shinagawa, Tomohiro Inoue

*Corresponding author for this work

    Research output: Chapter in Book/Report/Conference proceedingChapter

    1 Citation (Scopus)


    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 languageEnglish
    Title of host publicationBusiness Cycles in Economics: Types, Challenges and Impacts on Monetary Policies
    PublisherNova Science Publishers, Inc.
    Number of pages18
    ISBN (Print)9781633215382, 9781633213227
    Publication statusPublished - 2014 Jul 1


    • 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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