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 u″(x) + λ[ru(1 - u/q) - u/1 + mu + u2] = 0, -1 < x < 1, u(-1) = u(1) = 0, where the quantity in brackets is the growth rate function and λ > 0 is a bifurcation parameter. On the (λ, ǁuǁ∞)-plane, we give a complete classification of two qualitatively different bifurcation curves: a C-shaped curve and a monotone increasing curve.