International Journal of Economic Behavior and Organization
Volume 3, Issue 2-1, April 2015, Pages: 77-85
Received: Mar. 25, 2015;
Accepted: Mar. 25, 2015;
Published: Apr. 17, 2015
Views 3568 Downloads 146
Akio Matsumoto, Department of Economics, Chuo University, Higashi-Nakano, Hachioji, Tokyo, Japan
Ferenc Szidarovszky, Department of Applied Mathematics, University of Pécs, Ifjúság, u. 6, Pécs, Hungary
An elementary analysis is developed to determine the stability region of certain classes of ordinary differential equations with two delays. Our analysis is based on determining stability switches first where an eigenvalue is pure complex, and then checking the conditions for stability loss or stability gain. In the cases of both stability losses and stability gains Hopf bifurcation occurs giving the possibility of the birth of limit cycles.
Dynamic Economic Systems with Two Time Delays, International Journal of Economic Behavior and Organization. Special Issue: Recent Developments of Economic Theory and Its Applications.
Vol. 3, No. 2-1,
2015, pp. 77-85.
Bellman, R. and Cooke, K. (1963), Differential-Difference Equations. Academic Press, New York.
Gu, K., Niculescu, S. and Chen, J. (2005), On Stability Crossing Curves for General Systems with Two Delays. Journal of Mathematical Analysis and Applications, 311, 231-252.
Hayes, N. D. (1950), Roots of the Transcendental Equation Associated with a Certain Difference-Differential Equation. Journal of the London Mathematical Society, 25, 226-232.
Hale, J. (1979), Nonlinear Oscillations in Equations with Delays. In Nonlinear Oscillations in Biology (F. C. Hoppenstadt, ed.). Lectures in Applied Mathematics, 17, American Mathematical Society, 157-185.
Hale, J. and Huang, W. (1993), Global Geometry of the Stable Regions for Two Delay Differential Equations. Journal of Mathematical Analysis and Applications, 178, 344-362.
Matsumoto, A. and Szidarovszky, F. (2015), Nonlinear Multiplier-Acceelerator Model with Investment and Consumption Delay. Structural Change and Economic Dynamics, 33, 1-9.
Matsumoto, A. and Szidarovszky, F. (2013a), An Elementary Study of a Class of Dynamic Systems with Single Delay. CUBO A Mathematical Journal, 15, 1-7.
Matsumoto, A. and Szidarovszky, F. (2013b), Learning in Monopolies with Delayed Price Information. IERCH DP. No.203, Institute of Economic Research, Chuo University.
Matsumoto, A. and Szidarovszky, F. (2012), An Elementary Study of a Class of Dynamic Systems with Two Time Delays. CUBO A Mathematical Journal, 14, 103-113.
Phillips, A. (1954), Stabilization Policy in a Closed Economy. Economic Journal, 64, 290-323.