Asymptotic Behavior of a Delay Differential Neoclassical Growth Model

A neoclassical growth model is examined with a special mound-shaped production function. Continuous time scales are assumed and a complete steady state and stability analysis is presented. Fixed delay is then assumed and it is shown how the asymptotic stability of the steady state is lost if the del...

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Bibliographic Details
Published in:Sustainability 2013-02, Vol.5 (2), p.440-455
Main Authors: Matsumoto, Akio, Szidarovszky, Ferenc
Format: Article
Language:English
Subjects:
Applied mathematics
Growth models
Mathematical models
Production functions
Sustainability
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Summary:A neoclassical growth model is examined with a special mound-shaped production function. Continuous time scales are assumed and a complete steady state and stability analysis is presented. Fixed delay is then assumed and it is shown how the asymptotic stability of the steady state is lost if the delay reaches a certain threshold, where Hopf bifurcation occurs. In the case of continuously distriubuted delays, we show that with small average delays stability is preserved, then lost at a threshold, then it is regained if the average delay becomes sufficiently large. The occurence of Hopf bifurcation is shown at both critical values.
ISSN:2071-1050
2071-1050
DOI:10.3390/su5020440