On Impossibility of Limit Cycles in Certain Two-Dimensional Continuous-Time Growth Mode
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.
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Volume (Year): 5 (2001)
Issue (Month): 1 (April)
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