Hopf bifurcation and the stability of non-linear age-dependent population models

DOI10.1016/0898-1221(88)90280-5zbMath0649.92020OpenAlexW2026388026MaRDI QIDQ1106140

J. H. Swart

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1016/0898-1221(88)90280-5

zbMATH Keywords

Hopf bifurcationGurtin-MacCamy model of age-dependent population dynamicsstable orbits

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Population dynamics (general) (92D25) Partial differential equations of mathematical physics and other areas of application (35Q99) Bifurcations in context of PDEs (35B32)

Related Items (13)

Normal forms for an age structured model ⋮ 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 ⋮ Hopf bifurcation for a maturity structured population dynamic model ⋮ An age‐structured model of population dynamics with dominant ages, delayed behavior, and oscillations ⋮ Global positive periodic solutions of age-dependent competing systems ⋮ Bogdanov-Takens bifurcation in a predator-prey model ⋮ Oscillations and stability due to juvenile competitive effects on adult fertility ⋮ McKendrick-Tornquist age-dependent population model ⋮ Center manifolds for semilinear equations with non-dense domain and applications to Hopf bifurcation in age structured models ⋮ The age-dependent population model: numerical check of stability/instability of a steady state. ⋮ Hopf bifurcation for a spatially and age structured population dynamics model

Cites Work

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• Stability of biochemical reaction tanks
• The stability of a nonlinear, age dependent population model, as applied to a biochemical reaction tank
• Some simple models for nonlinear age-dependent population dynamics
• Non-linear age-dependent population dynamics

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