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-10$ 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.

Keywords

• bifurcation curve
• exact multiplicity
• diffusive logistic problem
• holling type-iv functional response
• time map