Bifurcation of time periodic solutions of the McKendrick equations with applications to population dynamics

DOI10.1016/0898-1221(83)90060-3zbMath0533.92014OpenAlexW1983431812MaRDI QIDQ790074

Jim M. Cushing

Publication date: 1983

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0898-1221(83)90060-3

zbMATH Keywords

nonlinear systemage-structured populationMcKendrick equationsgestation periodbifurcation of time periodic solutionssteady state instabilities

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Equations involving nonlinear operators (general) (47J05) Population dynamics (general) (92D25)

Related Items (18)

Equilibria in systems of interacting structured populations ⋮ Normal forms for an age structured model ⋮ On the relationship betweenrandR₀and its role in the bifurcation of stable equilibria of Darwinian matrix models ⋮ Hopf bifurcation theorem for second-order semi-linear Gurtin-MacCamy equation ⋮ A short proof for Hopf bifurcation in Gurtin-MacCamy’s population dynamics model ⋮ Hopf bifurcation for non-densely defined Cauchy problems ⋮ An age-dependent population model and its operator ⋮ Hopf bifurcation for a maturity structured population dynamic model ⋮ An age‐structured model of population dynamics with dominant ages, delayed behavior, and oscillations ⋮ A didactical note on the advantage of using two parameters in Hopf bifurcation studies ⋮ A nonlinear continuous-time model for a semelparous species ⋮ Existence and stability of equilibria in age-structured population dynamics ⋮ Dynamics of populations structured by internal variables ⋮ Hopf bifurcation in a size-structured population dynamic model with random growth ⋮ Center manifolds for semilinear equations with non-dense domain and applications to Hopf bifurcation in age structured models ⋮ Global branches of equilibrium solutions of the McKendrick equations for age-structured population growth ⋮ Hopf bifurcation for a spatially and age structured population dynamics model ⋮ Equilibria in structured populations

Cites Work

• Equilibrium solutions of age-specific population dynamics of several species
• Stability and bifurcation in age-dependent population dynamics
• On the theory and application of the Hopf-Friedrich Bifurcation theory
• The dynamics of density dependent population models
• Topics in stability and bifurcation theory
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