S-shaped and broken S-shaped bifurcation diagrams with hysteresis for a multiparameter spruce budworm population problem in one space dimension

DOI10.1016/j.jde.2013.05.004zbMath1287.34010OpenAlexW2166172062MaRDI QIDQ2435179

Shin-Hwa Wang, Tzung-Shin Yeh

Publication date: 3 February 2014

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2013.05.004

zbMATH Keywords

spruce budworm problem\(S\)-shaped bifurcation diagrambroken \(S\)-shaped bifurcation diagramstrong hysteresisweak hysteresis

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Population dynamics (general) (92D25) Ecology (92D40) Positive solutions to nonlinear boundary value problems for ordinary differential equations (34B18) Applications of boundary value problems involving ordinary differential equations (34B60) Parameter dependent boundary value problems for ordinary differential equations (34B08) Boundary eigenvalue problems for ordinary differential equations (34B09)

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Multiple spreading phenomena for a free boundary problem of a reaction-diffusion equation with a certain class of bistable nonlinearity ⋮ Classification of bifurcation curves of positive solutions for a nonpositone problem with a quartic polynomial ⋮ Multitype bistability and long transients in a delayed spruce budworm population model ⋮ Spatiotemporal patterns of a structured spruce budworm diffusive model ⋮ Unnamed Item ⋮ Asymptotic behavior of solutions for multi-stable equation with Dirichlet boundary condition ⋮ Entire solutions of the spruce budworm model ⋮ Classification of bifurcation diagrams for a multiparameter diffusive logistic problem with Holling type-IV functional response ⋮ S-shaped and broken S-shaped bifurcation curves for a multiparameter diffusive logistic problem with Holling type-III functional response ⋮ Bifurcation curves of positive steady-state solutions for a reaction-diffusion problem of lake eutrophication ⋮ Bifurcation analysis of a spruce budworm model with diffusion and physiological structures ⋮ Stability of a budworm growth model with random perturbations ⋮ Inverse bifurcation problems for diffusive Holling-Tanner population model

Cites Work

• A theorem on S-shaped bifurcation curve for a positone problem with convex-concave nonlinearity and its applications to the perturbed Gelfand problem
• Spatial patterning of the spruce budworm
• Mathematical biology. Vol. 1: An introduction.
• Mathematical biology. Vol. 2: Spatial models and biomedical applications.
• Persistence in reaction diffusion models with weak Allee effect
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