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[Solved] A model with an Allee effect from H. Thieme is below with N(t) being the population size at time t. The model is based on the fact that unmated

Question: A model with an Allee effect from H. Thieme is below with N(t) being the population size at time t. The model is based on the fact that unmated females must find a mate and during the time they are searching, before reproduction, they experience an increased mortality due to predation.

\(\left\{ \begin{aligned} & \frac{dN}{dt}=rN\left( 1-\frac{N}{K}-\frac{a}{1+bN} \right), \\ & N\left( 0 \right)={{N}_{0}} \\ \end{aligned} \right.\)

with No, r, a, b, K all positive parameter. We say that a forces the Allee effect.

Make the following change of variables: \(x=bN\) and \(\tau =rt\) to express the DE in dimensionless form.

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