Asymptotic formulas for $L^2$ bifurcation curves of nonlocal logistic equation of population dynamics

The one-dimensional nonlocal Kirchhoff type bifurcation problems which are derived from logistic equation of population dynamics are studied. We obtain the precise asymptotic shapes of $L^2$ bifurcation curves $\lambda =\lambda (\alpha )$ as $\alpha \to \mathrm{\infty }$, where $\alpha :=\mathrm{\parallel }{u}_{\lambda }{\mathrm{\parallel }}_2$.