Asymptotic behavior of bifurcation curves of nonlocal logistic equation of population dynamics

We study the one-dimensional nonlocal Kirchhoff type bifurcation problem related to logistic equation of population dynamics. We establish the precise asymptotic formulas for bifurcation curve $\lambda =\lambda (\alpha )$ as $\alpha \to \mathrm{\infty }$ in $L^2$-framework, where $\alpha :=\mathrm{\parallel }{u}_{\lambda }{\mathrm{\parallel }}_2$.