Invariant manifolds for Volterra integral equations of convolution type

DOI10.1016/0022-0396(84)90156-6zbMath0543.45004OpenAlexW1996002601MaRDI QIDQ796036

Stephan A. van Gils, Odo Diekmann

Publication date: 1984

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://ir.cwi.nl/pub/1861

zbMATH Keywords

Hopf bifurcationcenter manifoldpopulation biologyvariation-of-constants formulalocal semiflowsaddle point propertyconvolution type

Mathematics Subject Classification ID

Semigroups of nonlinear operators (47H20) Other nonlinear integral equations (45G10) Population dynamics (general) (92D25) Stability theory for integral equations (45M10) Volterra integral equations (45D05)

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Cycles in cannibalistic egg-larval interactions ⋮ Center manifolds and contractions on a scale of Banach spaces ⋮ Hopf bifurcation for functional and functional differential equations with infinite delay ⋮ Stability, multiplicity and global continuation of symmetric periodic solutions of a nonlinear Volterra integral equation ⋮ Volterra integral equations of the first kind and applications to linear diffusions ⋮ Extended Hopf bifurcation for abstract integral equations at resonant eigenvalue ⋮ Vintage capital, investment, and growth ⋮ Dangerous connections: on binding site models of infectious disease dynamics ⋮ An abstract approach to smoothness of invariant manifolds ⋮ A center manifold for second order semilinear differential equations on the real line and applications to the existence of wave trains for the Gurtin–McCamy equation ⋮ Stable Manifolds in the Method of Averaging ⋮ Center manifolds for semilinear equations with non-dense domain and applications to Hopf bifurcation in age structured models ⋮ Variation of constants formulae for forward and backward stochastic Volterra integral equations ⋮ Stability of the endemic equilibrium in epidemic models with subpopulations ⋮ Simple mathematical models for cannibalism: A critique and a new approach

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