On the qualitative behaviour of populations with age-specific interactions

DOI10.1016/0898-1221(83)90020-2zbMath0537.92017OpenAlexW2016907540MaRDI QIDQ792914

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)90020-2

zbMATH Keywords

fixed point theory asymptotic stability Hopf bifurcation existence of periodic solutions age structure linearization techniques density-dependent birth and death rates existence and stability of equilibrium solutions nonlinear model of population dynamics

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Periodic solutions to ordinary differential equations (34C25) Stability in context of PDEs (35B35) Population dynamics (general) (92D25) Bifurcations in context of PDEs (35B32)

Related Items (38)

Small perturbations in nonlinear age-structured population equations ⋮ Equilibria in systems of interacting structured populations ⋮ Normal forms for an age structured model ⋮ Logistic models of structured population growth ⋮ Periodic McKendrick equations for age-structered population growth ⋮ Preface. Special issue dedicated to Jan Prüss on the occasion of his 65th birthday ⋮ Hopf bifurcation theorem for second-order semi-linear Gurtin-MacCamy equation ⋮ Persistence and extinction in continuous age-structured population models ⋮ A short proof for Hopf bifurcation in Gurtin-MacCamy’s population dynamics model ⋮ Bifurcation of positive equilibria in nonlinear structured population models with varying mortality rates ⋮ Stability of a class of nonlinear hierarchical size-structured population model ⋮ Global continua of positive solutions for some quasilinear parabolic equation with a nonlocal initial condition ⋮ Hopf bifurcation for non-densely defined Cauchy problems ⋮ Dynamics of age-structured predator-prey population models ⋮ Hopf bifurcation for a maturity structured population dynamic model ⋮ A semigroup approach to the strong ergodic theorem of the multistate stable population process ⋮ A model of proliferating cell populations with correlation of mother- daughter mitotic times ⋮ An age-structured model for the transmission dynamics of hepatitis B: asymptotic analysis ⋮ Bogdanov-Takens bifurcation in a predator-prey model ⋮ Stability analysis for equilibria in age-specific population dynamics ⋮ Some results based on maximal regularity regarding population models with age and spatial structure ⋮ Global bifurcation of positive equilibria in nonlinear population models ⋮ Kermack and McKendrick revisited: The variable subsceptibility model for infectious deseases ⋮ Trajectory analysis of nonlinear kinetic models of population dynamics of several species ⋮ Hopf bifurcation for a predator-prey model with age structure ⋮ Periodic solutions for nonlinear equations of structured populations ⋮ Global stability of an age-structured population model on several temporally variable patches ⋮ 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 ⋮ Stability for a competing system of hierarchical age-structured populations ⋮ Center manifolds for semilinear equations with non-dense domain and applications to Hopf bifurcation in age structured models ⋮ On the stability of separable solutions of a sexual age-structured population dynamics model ⋮ The semigroup associated with nonlinear age dependent population dynamics ⋮ An age-dependent population dynamical model with a small parameter. ⋮ 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

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