A general method for computer-assisted proofs of periodic solutions in delay differential problems
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Publication:2134120
DOI10.1007/s10884-020-09908-6zbMath1504.34191OpenAlexW3096014207WikidataQ113901166 ScholiaQ113901166MaRDI QIDQ2134120
Jean-Philippe Lessard, Chris Groothedde, Jan Bouwe Van Den Berg
Publication date: 6 May 2022
Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10884-020-09908-6
periodic solutionsdelay differential equationsFourier seriescomputer-assisted proofscontraction mappingMackey-Glass equation
Applications of operator theory to differential and integral equations (47N20) Periodic solutions to functional-differential equations (34K13) Error analysis and interval analysis (65G99)
Related Items (7)
Validated integration of differential equations with state-dependent delay ⋮ A rigorous implicit \(C^1\) Chebyshev integrator for delay equations ⋮ Numerical Computation of Transverse Homoclinic Orbits for Periodic Solutions of Delay Differential Equations ⋮ Torus knot choreographies in the n-body problem ⋮ Numerical Computation of Periodic Orbits and Isochrons for State-Dependent Delay Perturbation of an ODE in the Plane ⋮ Numerical inclusion of exact periodic solutions for time delay Duffing equation ⋮ Parameterization Method for State-Dependent Delay Perturbation of an Ordinary Differential Equation
Uses Software
Cites Work
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- Construction of quasi-periodic solutions of state-dependent delay differential equations by the parameterization method. II: Analytic case.
- Efficient and generic algorithm for rigorous integration forward in time of dPDEs. I
- High-dimensional chaotic behavior in systems with time-delayed feedback
- A simple chaotic delay differential equation
- Rigorous numerics for dissipative PDEs. III: An effective algorithm for rigorous integration of dissipative PDEs
- Computational fixed-point theory for differential delay equations with multiple time lags
- Computer-assisted methods for the study of stationary solutions in dissipative systems, applied to the Kuramoto-Sivashinski equation
- A geometric method for infinite-dimensional chaos: symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line
- Periodic solutions of analytic functional differential equations are analytic
- On the nonlinear differential delay equation x'(t) = -f(x(t),x(t-1))
- The range of periods of periodic solutions of \(x'(t)=-\alpha f(x(t-1))\)
- Verified integration of ODEs and flows using differential algebraic methods on high-order Taylor models
- Introduction to functional differential equations
- Multiple solutions for a semilinear boundary value problem: a computational multiplicity proof.
- A rigorous ODE solver and Smale's 14th problem
- Algorithm for rigorous integration of delay differential equations and the computer-assisted proof of periodic orbits in the Mackey-Glass equation
- Parameterization method for unstable manifolds of delay differential equations
- Rigorous numerics for ill-posed PDEs: periodic orbits in the Boussinesq equation
- A proof of Wright's conjecture
- A proof of Jones' conjecture
- Global continuation and asymptotic behaviour for periodic solutions of a differential-delay equation
- Rigorous numerics for dissipative partial differential equations. II: Periodic orbit for the Kuramoto-Sivashinsky PDE -- a computer-assisted proof
- Delay equations. Functional-, complex-, and nonlinear analysis
- The Poincaré-Bendixson theorem for monotone cyclic feedback systems with delay
- Automatic differentiation for Fourier series and the radii polynomial approach
- Topics in delay differential equations
- Recent advances about the uniqueness of the slowly oscillating periodic solutions of Wright's equation
- Rigorous validation of stochastic transition paths
- Stability and uniqueness of slowly oscillating periodic solutions to Wright's equation
- NUMERICAL VERIFICATION METHODS FOR SOLUTIONS OF ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS
- Rigorous numerics for analytic solutions of differential equations: the radii polynomial approach
- Rigorous Numerics in Dynamics
- Global Attractivity of the Zero Solution for Wright's Equation
- Verification methods: Rigorous results using floating-point arithmetic
- Computer Assisted Fourier Analysis in Sequence Spaces of Varying Regularity
- Integration of Dissipative Partial Differential Equations: A Case Study
- A Software Package for the Numerical Integration of ODEs by Means of High-Order Taylor Methods
- Validated Continuation for Equilibria of PDEs
- A computer-assisted proof of the Feigenbaum conjectures
- The Lorenz attractor exists
- Chaos in the Lorenz equations: a computer-assisted proof
- A computer assisted proof of multiple periodic orbits in some first order non-linear delay differential equation
- Oscillation and Chaos in Physiological Control Systems
- Wright's equation has no solutions of period four
- A Framework for the Numerical Computation and A Posteriori Verification of Invariant Objects of Evolution Equations
- Validation of the bifurcation diagram in the 2D Ohta–Kawasaki problem
- On the Stability of a Periodic Solution of a Differential Delay Equation
- Interaction of maturation delay and nonlinear birth in population and epidemic models
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