Effective methods for recurrence solutions in delay differential equations

Autor/a

Gimeno i Alquézar, Joan

Director/a

Jorba i Monte, Àngel

De la Llave, Rafael, 1957-

Tutor/a

Jorba i Monte, Àngel

Data de defensa

2020-01-08

Pàgines

134 p.



Departament/Institut

Universitat de Barcelona. Departament de Matemàtiques i Informàtica

Resum

This thesis deals with the jet transport for numerical integrators and the effective invariant object computation of delay differential equations. Firstly we study how automatic differentiation (AD) affects when they are applied to numerical integrators of ordinary differential equations (ODEs). We prove that the use of AD is exactly the same as considering the initial ODE and add new equations to the calculation of the variational flow up to a certain order. With this result we propose to detail the effective computation when these equations are affected by a delay. In particular, the computation of the stability of equilibrium points, the computation of periodic orbits as well as their stability and continuation. Similarly the computation of quasi-orbits periodic and its stability. For such computations, we avoid the explicit generation of the Jacobian matrix and we only require the matrix-vector evaluation. Finally, we cover the existence, uniqueness and numerical computation of the slowest direction of the stable manifold of a limit cycle of a state-dependent delay equation differential. The results are formulated in a posteriori format, which leads to rigorous proofs of numerical experiments. Specifically our result is applicable when you have a delayed perturbation and it depends on the state of an ODE in the plane.

Paraules clau

Equacions diferencials retardades; Ecuaciones diferenciales con argumento retardado; Delay differential equations

Matèries

51 - Matemàtiques

Àrea de coneixement

Ciències Experimentals i Matemàtiques

Documents

JGA_PhD-THESIS.pdf

1.596Mb

 

Drets

L'accés als continguts d'aquesta tesi queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: http://creativecommons.org/licenses/by-sa/4.0/
L'accés als continguts d'aquesta tesi queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: http://creativecommons.org/licenses/by-sa/4.0/

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