Complete classification of bifurcation curves for a multiparameter diffusive logistic problem with generalized Holling type-IV functional response
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Date
2021-02-23
Authors
Ciou, Jyun-Yuan
Yeh, Tzung-Shin
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
Bifurcation curve, Exact multiplicity, Diffusive logistic problem, Holling type-IV functional response, Time map
Citation
Ciou, J. Y., & Yeh, T. S. (2021). Complete classification of bifurcation curves for a multiparameter diffusive logistic problem with generalized Holling type-IV functional response. <i>Electronic Journal of Differential Equations, 2021</i>(10), pp. 1-12.
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Attribution 4.0 International