Complete classification of bifurcation curves for a multiparameter diffusive logistic problem with generalized Holling type-IV functional response

Abstract

We study exact multiplicity and bifurcation curves of positive solutions for the diffusive logistic problem with generalized Holling type-IV functional response $$\displaylines{ u''(x)+\lambda \big[ ru(1-\frac{u}{q})-\frac{u}{1+mu+u^2}\big] =0,\quad-1<x<1, \cr u(-1)=u(1)=0, }$$ where the quantity in brackets is the growth rate function and \(\lambda >0\) is a bifurcation parameter. On the \((\lambda ,||u||_{\infty })\)-plane, we give a complete classification of two qualitatively different bifurcation curves: a C-shaped curve and a monotone increasing curve.
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