| Peer-Reviewed

Dynamic Economic Systems with Two Time Delays

Received: 25 March 2015     Accepted: 25 March 2015     Published: 17 April 2015
Views:       Downloads:
Abstract

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.

Published in International Journal of Economic Behavior and Organization (Volume 3, Issue 2-1)

This article belongs to the Special Issue Recent Developments of Economic Theory and Its Applications

DOI 10.11648/j.ijebo.s.2015030201.22
Page(s) 77-85
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Multiple Delays, Monopoly Model, Multiplier-Accelerator Model, Double-Edged Effect on Stability

References
[1] Bellman, R. and Cooke, K. (1963), Differential-Difference Equations. Academic Press, New York.
[2] 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.
[3] 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.
[4] 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.
[5] 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.
[6] Matsumoto, A. and Szidarovszky, F. (2015), Nonlinear Multiplier-Acceelerator Model with Investment and Consumption Delay. Structural Change and Economic Dynamics, 33, 1-9.
[7] 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.
[8] Matsumoto, A. and Szidarovszky, F. (2013b), Learning in Monopolies with Delayed Price Information. IERCH DP. No.203, Institute of Economic Research, Chuo University.
[9] 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.
[10] Phillips, A. (1954), Stabilization Policy in a Closed Economy. Economic Journal, 64, 290-323.
Cite This Article
  • APA Style

    Akio Matsumoto, Ferenc Szidarovszky. (2015). Dynamic Economic Systems with Two Time Delays. International Journal of Economic Behavior and Organization, 3(2-1), 77-85. https://doi.org/10.11648/j.ijebo.s.2015030201.22

    Copy | Download

    ACS Style

    Akio Matsumoto; Ferenc Szidarovszky. Dynamic Economic Systems with Two Time Delays. Int. J. Econ. Behav. Organ. 2015, 3(2-1), 77-85. doi: 10.11648/j.ijebo.s.2015030201.22

    Copy | Download

    AMA Style

    Akio Matsumoto, Ferenc Szidarovszky. Dynamic Economic Systems with Two Time Delays. Int J Econ Behav Organ. 2015;3(2-1):77-85. doi: 10.11648/j.ijebo.s.2015030201.22

    Copy | Download

  • @article{10.11648/j.ijebo.s.2015030201.22,
      author = {Akio Matsumoto and Ferenc Szidarovszky},
      title = {Dynamic Economic Systems with Two Time Delays},
      journal = {International Journal of Economic Behavior and Organization},
      volume = {3},
      number = {2-1},
      pages = {77-85},
      doi = {10.11648/j.ijebo.s.2015030201.22},
      url = {https://doi.org/10.11648/j.ijebo.s.2015030201.22},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijebo.s.2015030201.22},
      abstract = {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.},
     year = {2015}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Dynamic Economic Systems with Two Time Delays
    AU  - Akio Matsumoto
    AU  - Ferenc Szidarovszky
    Y1  - 2015/04/17
    PY  - 2015
    N1  - https://doi.org/10.11648/j.ijebo.s.2015030201.22
    DO  - 10.11648/j.ijebo.s.2015030201.22
    T2  - International Journal of Economic Behavior and Organization
    JF  - International Journal of Economic Behavior and Organization
    JO  - International Journal of Economic Behavior and Organization
    SP  - 77
    EP  - 85
    PB  - Science Publishing Group
    SN  - 2328-7616
    UR  - https://doi.org/10.11648/j.ijebo.s.2015030201.22
    AB  - 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.
    VL  - 3
    IS  - 2-1
    ER  - 

    Copy | Download

Author Information
  • Department of Economics, Chuo University, Higashi-Nakano, Hachioji, Tokyo, Japan

  • Department of Applied Mathematics, University of Pécs, Ifjúság, u. 6, Pécs, Hungary

  • Sections