Finite population fluctuations may not destroy bistability in growing population models.
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Analysis of the model in density space instead of the number of units space avoids numerical problems.
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Hysteresis cycle is found in the model.
Abstract
We study the role of the finite number of units in a three state model with a growing population. The model presents two attractors, namely a fixed point and a limit cycle. In the mean field approximation, it has been shown that there is a bistability region for which both attractors are stable. We observe that, contrary to constant population models, the bistability is preserved in the presence of finite number fluctuations.
