= Overcompensation in a population model
Overcompensation occurs when a larger present population produces a smaller total population in the next generation over part of the relevant range. It is stronger than a decline of per-capita growth alone. For $F(u)=\alpha u/(\beta+u^\gamma)$ with $\gamma>1$, the large-abundance response $F(u)\sim\alpha u^{1-\gamma}$ decreases with abundance. Stronger feedback can drive a fixed-point multiplier through minus one, but that local threshold alone does not establish chaotic behaviour.
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