Electron. J. Differential Equations, Vol. 2021 (2021), No. 10, pp. 1-12.

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

Jyun-Yuan Ciou, Tzung-Shin Yeh

Abstract:
We study exact multiplicity and bifurcation curves of positive solutions for the diffusive logistic problem with generalized Holling type-IV functional response

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.

Submitted April 5, 2019. Published February 23, 2021.
Math Subject Classifications: 34B15, 34B18.
Key Words: Bifurcation curve; exact multiplicity; diffusive logistic problem; Holling type-IV functional response; time map.
DOI: https://doi.org/10.58997/ejde.2021.10

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Jyun-Yuan Ciou
Department of Applied Mathematics
National University of Tainan
Tainan 700, Taiwan ROC
email: b7626529@gmail.com
Tzung-Shin Yeh
Department of Applied Mathematics
National University of Tainan
Tainan 700, Taiwan, ROC
email: tsyeh@mail.nutn.edu.tw

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