Approximation of eigenvalues of evolution operators for linear coupled renewal and retarded functional differential equations

Recently, systems of coupled renewal and retarded functional differential equations have begun to play a central role in complex and realistic models of population dynamics. In view of studying the local asymptotic stability of equilibria and (mainly) periodic solutions, we propose a pseudospectral...

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Bibliographic Details
Published in:Ricerche di matematica Vol. 69; no. 2; pp. 457 - 481
Main Authors: Breda, Dimitri, Liessi, Davide
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.11.2020
Subjects:
Algebra
Analysis
Geometry
Mathematics
Mathematics and Statistics
Numerical Analysis
Probability Theory and Stochastic Processes
34K30
65L03
Retarded functional differential equations
Stability
65L15
65R20
65L07
Renewal equations
Eigenvalue approximation
Pseudospectral collocation
47D06
45C05
34L16
47D99
45D05
Equilibria and periodic solutions
Evolution operators
ISSN:0035-5038, 1827-3491
Online Access:Get full text
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Summary:Recently, systems of coupled renewal and retarded functional differential equations have begun to play a central role in complex and realistic models of population dynamics. In view of studying the local asymptotic stability of equilibria and (mainly) periodic solutions, we propose a pseudospectral collocation method to approximate the eigenvalues of the evolution operators of linear coupled equations, providing rigorous error and convergence analyses and numerical tests. The method combines the ideas of the analogous techniques developed separately for renewal equations and for retarded functional differential equations. Coupling them is not trivial, due to the different state spaces of the two classes of equations, as well as to their different regularization properties.
ISSN:0035-5038
1827-3491
DOI:10.1007/s11587-020-00513-9