Global branches of equilibrium solutions of the McKendrick equations for age-structured population growth

DOI10.1016/0898-1221(85)90145-2zbMath0578.92020OpenAlexW2013864669MaRDI QIDQ1066839

Jim M. Cushing

Publication date: 1985

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

Full work available at URL: https://doi.org/10.1016/0898-1221(85)90145-2

zbMATH Keywords

global bifurcationpopulation growthage-structured populationMcKendrick equationsnet reproductive ratepositive equilibriacontinuity assumptionsdensity dependent death and fertility ratesexistence of equilibrium solutions

Mathematics Subject Classification ID

Population dynamics (general) (92D25) Bifurcations in context of PDEs (35B32)

Related Items (12)

Evolution problems with nonlinear nonlocal boundary conditions ⋮ Equilibria in systems of interacting structured populations ⋮ Bifurcation of positive equilibria in nonlinear structured population models with varying mortality rates ⋮ Net reproduction functions for nonlinear structured population models ⋮ Backward bifurcations and strong Allee effects in matrix models for the dynamics of structured populations ⋮ Oscillations and stability due to juvenile competitive effects on adult fertility ⋮ Some results based on maximal regularity regarding population models with age and spatial structure ⋮ Global bifurcation of positive equilibria in nonlinear population models ⋮ Existence and stability of equilibria in age-structured population dynamics ⋮ On positive solutions of some system of reaction-diffusion equations with nonlocal initial conditions ⋮ A global bifurcation theorem for Darwinian matrix models ⋮ Equilibria in structured populations

Cites Work

• Existence and stability of equilibria in age-structured population dynamics
• Bifurcation of time periodic solutions of the McKendrick equations with applications to population dynamics
• On the qualitative behaviour of populations with age-specific interactions
• Local and global stability for the solutions of a nonlinear renewal equation
• Non-linear age-dependent population growth
• Equilibrium solutions of age-specific population dynamics of several species
• On the global stability of the logistic age-dependent population growth
• Non-linear age-dependent population dynamics
• Some global results for nonlinear eigenvalue problems
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