Existence and stability of business cycles

Author:

Dohtani Akitaka

Abstract

We provide several sufficient conditions for the existence and the stability of limit cycles in two-dimensional differential equation systems. We also apply our results to business cycle models in the Keynesian tradition.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics

Reference20 articles.

1. J.P. Benassy, A non-Walrasian model of the business cycle, J. Econom. Behavior Org. 5, 77–89 (1984)

2. L. Cesari, Asymptotic Behavior and Stability Problems in Ordinary Differential Equations, Ergebnisse der Mathematik und ihrer Grenzgebiete, 2nd ed., Springer-Verlag, Berlin-Gottingen-Heidelberg, 1959

3. W. W. Chang and D. J. Smyth, The existence and persistence of cycles in a non-linear model: Kaldor’s 1940 model re-examined, Rev. Econom. Stud. 38, 37–44 (1971)

4. A. F. Filippov, A sufficient condition for the existence of a stable limit cycle for a second order equation, Mat. Sb. 30, 171–180 (1952) (Russian)

5. G. Gabisch and H.-W. Lorenz, Business Cycle Theory, Lecture Notes in Econom. Math. Systems, Vol. 283, Springer-Verlag, Berlin, 1987

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