Equations with infinite delay: numerical bifurcation analysis via pseudospectral discretization

DOI10.1016/j.amc.2018.03.104zbMath1427.65098OpenAlexW2801308095WikidataQ129355637 ScholiaQ129355637MaRDI QIDQ2335165

Mats Gyllenberg, Francesca Scarabel, Rossana Vermiglio

Publication date: 13 November 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2018.03.104

zbMATH Keywords

delay differential equationsinfinite delayVolterra integral equationsrenewal equationsphysiologically structured population modelsfinite dimensional state representationLaguerre pseudospectral discretization

Mathematics Subject Classification ID

Dynamical systems in biology (37N25) Population dynamics (general) (92D25) Computational methods for bifurcation problems in dynamical systems (37M20) Numerical methods for functional-differential equations (65L03)

Related Items

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Uses Software

• MATCONT
• OPQ
• Differentiation Matrix Suite

Cites Work

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• Dangerous connections: on binding site models of infectious disease dynamics
• Daphnia revisited: Local stability and bifurcation theory for physiologically structured population models explained by way of an example
• Equations with infinite delay: blending the abstract and the concrete
• Discrete or distributed delay? Effects on stability of population growth
• Perturbation theory for dual semigroups. I. The sun-reflexive case
• Introduction to functional differential equations
• Non-linear age-dependent population dynamics
• Delay equations. Functional-, complex-, and nonlinear analysis
• Semi-groups of nonlinear contractions and dissipative sets
• Spectral Methods
• Stability of Linear Delay Differential Equations
• On the formulation of epidemic models (an appraisal of Kermack and McKendrick)
• Stability of a Nonlinear Age-Dependent Population Model Containing a Control Variable
• Computing the Eigenvalues of Realistic Daphnia Models by Pseudospectral Methods
• Pseudospectral Discretization of Nonlinear Delay Equations: New Prospects for Numerical Bifurcation Analysis
• Interpolation Processes
• Mathematical aspects of physiologically structured populations: the contributions of J. A. J. Metz
• Perturbation theory for dual semigroups II. Time-dependent perturbations in the sun-reflexive case
• Generation of Pseudospectral Differentiation Matrices I
• Numerical bifurcation analysis of a class of nonlinear renewal equations
• MATCONT
• Pseudospectral Differencing Methods for Characteristic Roots of Delay Differential Equations
• Generation of Semi-Groups of Nonlinear Transformations on General Banach Spaces
• Approximation of Eigenvalues of Evolution Operators for Linear Renewal Equations