IJPAM: Volume 55, No. 3 (2009)

PARAMETRIC STABILITY OF THE SOLUTIONS OF
THE IMPULSIVE DIFFERENTIAL SOLOW EQUATION
WITH DELAY AND DYNAMIC THRESHOLD EFFECTS

Ivanka M. Stamova$^1$, Jean-François Emmenegger$^2$
$^1$Department of Mathematics
Bourgas Free University
62, San Stefano Str., Bourgas, 8000, BULGARIA
e-mail: istamova@abv.bg
$^2$Department of Quantitative Economics
University of Fribourg
90, Boulevard de Pérolles, Fribourg, 1700, SWITZERLAND
e-mail: jean-francois.emmenegger@unifr.ch


Abstract.The framework of the more than 50 years old Solow growth theory (1956) and Solow's studies on technical change (1957) have not lost their attraction and have been extended widely into modern growth theories. In this paper, the existence of jumps and threshold effects in German capital intensity is identified. For this reason an extension of the initial Solow equation towards a general impulsive Solow differential equation with a delay function is proposed. This extention is aimed to be applied in modern growth theories, for instance to model the German capital intensity. Sufficient conditions for the parametric stability of the solutions of such systems are investigated. The main results are obtained by applying the Lyapunov method.

``As long as we insist on practicing macro-economics
we shall need aggregate relationships."
Robert M. Solow (1957)


Received: June 30, 2009

AMS Subject Classification: 34K45, 91B84

Key Words and Phrases: stability, Lyapunov-Razumikhin function, impulsive functional differential Solow equation, macroeconomic time series, capital intensity, random walk, unit root, variance ratio statistic

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 55
Issue: 3