On Impossibility of Limit Cycles in Certain Two-Dimensional Continuous-Time Growth Mode

Sergey Slobodyan

Studies in Nonlinear Dynamics & Econometrics, 2001, vol. 5, issue 1, 9

Abstract: This article proves that periodic trajectories are generically impossible in a class of continuous-time growth models that allow a locally indeterminate steady state. Those models reducible to the two-dimensional Lotka-Volterra system of equations constitute the class considered here. Knowledge of the presence or absence of the limit cycles allows a global phase diagram of the system to be constructed. In particular, an explosive steady state implies that all perfect-foresight trajectories diverge to infinity and that the model cannot be used even locally.

Keywords: indeterminacy; limit cycles (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (2)

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DOI: 10.2202/1558-3708.1069

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