Stability and Bifurcation Analysis of Volterra Functional Equations in the Light of Suns and Stars
From MaRDI portal
Publication:3516110
DOI10.1137/060659211zbMath1149.39021OpenAlexW2045055369MaRDI QIDQ3516110
Mats Gyllenberg, Odo Diekmann, Philipp Getto
Publication date: 1 August 2008
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://semanticscholar.org/paper/c40ac08b6ebce636bca8286cbdcb3ffcba9fec85
Hopf bifurcationdelay differential equationscenter manifolddual semigroupprinciple of linearized stabilityVolterra functional equationsphysiologically structured populationsLipschitz perturbationssun-star-calculus
One-parameter semigroups and linear evolution equations (47D06) Population dynamics (general) (92D25) Stability, separation, extension, and related topics for functional equations (39B82) Stability theory of functional-differential equations (34K20) Bifurcation theory of functional-differential equations (34K18)
Related Items
Finite dimensional state representation of linear and nonlinear delay systems, Systems of populations with multiple structures: modeling and analysis, Approximation of eigenvalues of evolution operators for linear coupled renewal and retarded functional differential equations, Effect of parental care and aggregation on population dynamics, Piecewise discretization of monodromy operators of delay equations on adapted meshes, Long-time behavior of a size-structured population model with diffusion and delayed birth process, Computing the Eigenvalues of Realistic Daphnia Models by Pseudospectral Methods, 15 Years or So of Pseudospectral Collocation Methods for Stability and Bifurcation of Delay Equations, Numerical equilibrium analysis for structured consumer resource models, Asymptotic analysis of a size-structured cannibalism population model with delayed birth process, Pseudospectral Discretization of Nonlinear Delay Equations: New Prospects for Numerical Bifurcation Analysis, Semilinear formulation of a hyperbolic system of partial differential equations, Daphnia revisited: Local stability and bifurcation theory for physiologically structured population models explained by way of an example, Solvability of integral equations with endogenous delays, On the formulation of size-structured consumer resource models (with special attention for the principle of linearized stability), Asymptotic behaviors of a size-structured population model, Modelling physiologically structured populations: renewal equations and partial differential equations, Stability patterns for a size-structured population model and its stage-structured counterpart, Daphnias: from the individual based model to the large population equation, On local bifurcations in neural field models with transmission delays, In honour of Odo Diekmann on the occasion of his 65th birthday, Stochastic simulation of structured skin cell population dynamics, Piecewise orthogonal collocation for computing periodic solutions of renewal equations, Size-structured populations: immigration, (bi)stability and the net growth rate, Asymptotic analysis of a spatially and size-structured population model with delayed birth process, Steady state analysis of a nonlinear renewal equation, Mathematical aspects of physiologically structured populations: the contributions of J. A. J. Metz, Pseudospectral discretization of delay differential equations in sun-star formulation: results and conjectures, Numerical continuation and delay equations: a novel approach for complex models of structured populations, Stability analysis for a size-structured juvenile-adult population model, Asymptotic behavior of a hierarchical size-structured population model, Equations with infinite delay: blending the abstract and the concrete, Long-Time Behavior of Spatially and Size-Structured Population Dynamics with Delayed Birth Process, Asymptotic analysis of a size-structured population model with infinite states-at-birth, Adaptive dynamics for physiologically structured population models, Delay-induced blow-up in a planar oscillation model, Mathematical study on kinetics of hematopoietic stem cells – theoretical conditions for successful transplantation, On the formulation of epidemic models (an appraisal of Kermack and McKendrick), A numerical approach for investigating the stability of equilibria for structured population models, A didactical note on the advantage of using two parameters in Hopf bifurcation studies, OPTIMAL LATENT PERIOD IN A BACTERIOPHAGE POPULATION MODEL STRUCTURED BY INFECTION-AGE, Global stability properties of a class of renewal epidemic models, Semigroup Approaches of Cell Proliferation Models, Effect of density dependence on coinfection dynamics, Functional differential equation with infinite delay in a space of exponentially bounded and uniformly continuous functions, Dangerous connections: on binding site models of infectious disease dynamics, Numerical bifurcation analysis of physiologically structured populations: consumer-resource, cannibalistic and trophic models, Stability analysis of an enteropathogen population growing within a heterogeneous group of animals, Projectors on the generalized eigenspaces for functional differential equations using integrated semigroups, Approximation of Eigenvalues of Evolution Operators for Linear Renewal Equations, Evolution of density-dependent dispersal in a structured metapopulation, Twin semigroups and delay equations, A nonlinear structured population model: Lipschitz continuity of measure-valued solutions with respect to model ingredients, The Second Half-With a Quarter of a Century Delay, Mathematical model of malaria transmission dynamics with distributed delay and a wide class of nonlinear incidence rates, Floquet theory and stability of periodic solutions of renewal equations, Numerical bifurcation analysis of renewal equations via pseudospectral approximation, Ecology and evolution of symbiosis in metapopulations, Linearization of solution operators for state-dependent delay equations: a simple example, Qualitative Analysis of a PDE Model of Telomere Loss in a Proliferating Cell Population in the Light of Suns and Stars, On models of physiologically structured populations and their reduction to ordinary differential equations, How fast is the linear chain trick? A rigorous analysis in the context of behavioral epidemiology, Switching to Nonhyperbolic Cycles from Codimension Two Bifurcations of Equilibria of Delay Differential Equations, Stability analysis of a state-dependent delay differential equation for cell maturation: analytical and numerical methods, Asymptotic behavior of an integral equation of cell cycle model in the light of suns and stars, Center manifolds for semilinear equations with non-dense domain and applications to Hopf bifurcation in age structured models, Asymptotic behavior of an age-structured prey-predator system with distributed delay, NOTE ON THE UNIQUENESS OF AN ENDEMIC EQUILIBRIUM OF AN EPIDEMIC MODEL WITH BOOSTING OF IMMUNITY, Structured populations with distributed recruitment: from PDE to delay formulation, Modelling and optimising healthcare interventions in a model with explicit within- and between-host dynamics, Delay equation formulation of a cyclin-structured cell population model, Pseudospectral methods for the stability analysis of delay equations. I: The infinitesimal generator approach, Pseudospectral methods for the stability analysis of delay equations. II: The solution operator approach, Persistence versus extinction for a class of discrete-time structured population models, On the characteristic equation \(\lambda =\alpha_{1}+(\alpha_{2}+\alpha_{3}\lambda)e^{-\lambda}\) and its use in the context of a cell population model
