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 |
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Keywords
- Adjustment costs of investment
- Chaos
- Homoclinic orbit
- Hopf bifurcation
- Period doubling bifurcation
ASJC Scopus subject areas
- Business, Management and Accounting(all)
Cite this
Coefficient criterion for shil'nikov chaos : Application to a simple investment model. / Tsuzuki, Eiji; Shinagawa, Shunsuke; Inoue, Tomohiro.
Business Cycles in Economics: Types, Challenges and Impacts on Monetary Policies. Nova Science Publishers, Inc., 2014. p. 69-86.Research output: Chapter in Book/Report/Conference proceeding › Chapter
}
TY - CHAP
T1 - Coefficient criterion for shil'nikov chaos
T2 - Application to a simple investment model
AU - Tsuzuki, Eiji
AU - Shinagawa, Shunsuke
AU - Inoue, Tomohiro
PY - 2014/7/1
Y1 - 2014/7/1
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.
KW - Adjustment costs of investment
KW - Chaos
KW - Homoclinic orbit
KW - Hopf bifurcation
KW - Period doubling bifurcation
UR - http://www.scopus.com/inward/record.url?scp=84952887227&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84952887227&partnerID=8YFLogxK
M3 - Chapter
AN - SCOPUS:84952887227
SN - 9781633215382
SN - 9781633213227
SP - 69
EP - 86
BT - Business Cycles in Economics: Types, Challenges and Impacts on Monetary Policies
PB - Nova Science Publishers, Inc.
ER -