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Sustainability 2013, 5(2), 440-455; doi:10.3390/su5020440

Article

Asymptotic Behavior of a Delay Differential Neoclassical Growth Model

Akio Matsumoto ^1,*  and Ferenc Szidarovszky ²

¹ Department of Economics, Chuo University, 742-1, Higashi-Nakano, Hachioji, Tokyo, 192-0393, Japan ² Department of Applied Mathematics, University of Pecs, Ifjusag u. 6, H-7624, Pecs, Hungary

* Author to whom correspondence should be addressed.

Received: 27 November 2012; in revised form: 17 January 2013 / Accepted: 22 January 2013 / Published: 31 January 2013

(This article belongs to the Special Issue 40th Anniversary of 'The Limits to Growth')

Download PDF Full-Text [687 KB, uploaded 31 January 2013 10:29 CET]

Abstract: 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.

Keywords: neoclassical growth model; fixed time delay; Hopf bifurcation

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