Imperfect and Bogdanov-Takens bifurcations in biological models: from harvesting of species to isolation of infectives

DOI10.1007/s00285-023-01951-3zbMath1525.34077OpenAlexW4382011124MaRDI QIDQ6110194

Shigui Ruan, Dongmei Xiao

Publication date: 4 July 2023

Published in: Journal of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00285-023-01951-3

zbMATH Keywords

predator-prey modelepidemic modelBogdanov-Takens bifurcationimperfect bifurcationsimportation/isolationstocking/harvesting

Mathematics Subject Classification ID

Epidemiology (92D30) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Population dynamics (general) (92D25) Qualitative investigation and simulation of ordinary differential equation models (34C60) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (2)

Periodic dynamics of a single species model with seasonal Michaelis-Menten type harvesting. II: Existence of two periodic solutions ⋮ Effects of whaling and krill fishing on the whale-krill predation dynamics: bifurcations in a harvested predator-prey model with Holling type I functional response

Cites Work

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• Bifurcation from a degenerate simple eigenvalue
• Analysis of SIR epidemic models with nonlinear incidence rate and treatment
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Maximum sustainable yields in systems subject to harvesting at more than one trophic level
• Constant-rate stocking of predator-prey systems
• Coexistence properties of some predator-prey systems under constant rate harvesting and stocking
• An analysis of an ordinary differential equation model for a two-species predator-prey system with harvesting and stocking
• Stability regions and transition phenomena for harvested predator-prey systems
• Stability regions in predator-prey systems with constant-rate prey harvesting
• Elements of applied bifurcation theory.
• Bifurcations in an epidemic model with constant removal rate of the infectives
• Modeling the importation and local transmission of vector-borne diseases in Florida: the case of Zika outbreak in 2016
• Recurrent outbreaks of childhood diseases revisited: The impact of isolation
• Persistence and bifurcation of degenerate solutions
• Simulating the SARS outbreak in Beijing with limited data
• Bifurcation, perturbation of simple eigenvalues, and linearized stability
• The effect of immigration of infectives on disease-free equilibria
• Imperfect transcritical and pitchfork bifurcations
• Bifurcation from simple eigenvalues
• Stabilization and de-stabilization of predator-prey systems under harvesting and nutrient enrichment
• A theory for imperfect bifurcation via singularity theory
• Modeling the Effectiveness of Isolation Strategies in Preventing STD Epidemics
• Perturbed bifurcation theory
• Models for transmission of disease with immigration of infectives

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