In logistic model (12) consider small deviations from the equilibrium, i.e. when the solution is

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Step 1:u000ALetu0027s recall the logistic model (12), which is typically given by:u000A$$u005Cfrac{dN}{dt} u003D rNu005C

In logistic model (12) consider small deviations from the equilibrium, i.e. when the solution is $N(t)=N_p+\delta N(t)$, where $|\delta N(t)| \ll N p$. Show that for $\delta N(t)$ in the first approximation the linear Malthus model (10) is valid.