Pseudospectral reduction to compute Lyapunov exponents of delay differential equations

DOI10.3934/dcdsb.2018092zbMath1401.37091OpenAlexW2794155378WikidataQ129475158 ScholiaQ129475158MaRDI QIDQ1670360

Sara Della Schiava, Dimitri Breda

Publication date: 5 September 2018

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2018092

zbMATH Keywords

Lyapunov exponentsdelay differential equationspseudospectral methods

Mathematics Subject Classification ID

Numerical investigation of stability of solutions to ordinary differential equations (65L07) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25) Numerical methods for functional-differential equations (65L03)

Related Items (2)

15 Years or So of Pseudospectral Collocation Methods for Stability and Bifurcation of Delay Equations ⋮ Pseudospectral methods for the stability analysis of delay equations. II: The solution operator approach

Uses Software

• Matlab
• dde23

Cites Work

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• Low-dimensional Galerkin approximations of nonlinear delay differential equations
• A simple chaotic delay differential equation
• Nonautonomous delay differential equations in Hilbert spaces and Lyapunov exponents
• Chaotic attractors of an infinite-dimensional dynamical system
• Semigroups of linear operators and applications to partial differential equations
• Spline approximations for functional differential equations
• A family of embedded Runge-Kutta formulae
• Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing all of them. I: Theory
• A uniformly differentiable approximation scheme for delay systems using splines
• Introduction to functional differential equations
• Exponential decay of power spectra at high frequency and positive Lyapunov exponents
• Numerical solution of retarded functional differential equations as abstract Cauchy problems.
• Evaluation of the largest Lyapunov exponent in dynamical systems with time delay
• Delay equations. Functional-, complex-, and nonlinear analysis
• Computation of a few Lyapunov exponents for continuous and discrete dynamical systems
• Numerical solution of constant coefficient linear delay differential equations as abstract Cauchy problems
• Approximating Lyapunov exponents and Sacker-Sell spectrum for retarded functional differential equations
• Pseudospectral approximation of eigenvalues of derivative operators with nonlocal boundary conditions
• Approximation of Eigenvalues of Evolution Operators for Linear Retarded Functional Differential Equations
• On the Compuation of Lyapunov Exponents for Continuous Dynamical Systems
• Stability of Linear Delay Differential Equations
• Pseudospectral Discretization of Nonlinear Delay Equations: New Prospects for Numerical Bifurcation Analysis
• The Stability of Pseudospectral-Chebyshev Methods
• One-Parameter Semigroups for Linear Evolution Equations
• Spectral Methods in MATLAB
• Numerical bifurcation analysis of a class of nonlinear renewal equations
• Oscillation and Chaos in Physiological Control Systems
• Orthogonal Polynomials With Weight Function (1 - x)^α( l + x)^β + Mδ(x + 1) + Nδ(x - 1)
• Lyapunov Spectral Intervals: Theory and Computation
• Numerical Methods for Delay Differential Equations
• Pseudospectral Differencing Methods for Characteristic Roots of Delay Differential Equations
• Solving DDEs in Matlab

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