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.

Recommended Citation

Sergey Slobodyan (2001) "On Impossibility of Limit Cycles in Certain Two-Dimensional Continuous-Time Growth Mode ", Studies in Nonlinear Dynamics & Econometrics: Vol. 5: No. 1, Article 3.
http://www.bepress.com/snde/vol5/iss1/art3