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Computation of limit cycles and their isochrons: Fast algorithms and their convergence

Autor
Huguet, G.; de la Llave, R.
Tipus d'activitat
Article en revista
Revista
SIAM journal on applied dynamical systems
Data de publicació
2013
Volum
12
Número
4
Pàgina inicial
1763
Pàgina final
1802
DOI
https://doi.org/10.1137/120901210 Obrir en finestra nova
Projecte finançador
DINAMICA ASOCIADA A CONEXIONES ENTRE OBJETOS INVARIANTES, ASTRODINÁMICA, NEUROCIENCIA Y OTRAS APLICACIONES
DINAMICA ASOCIADA A CONEXIONES ENTRE OBJETOS INVARIANTES. APLICACIONES A
Repositori
http://hdl.handle.net/2117/22392 Obrir en finestra nova
Resum
We present efficient algorithms to compute limit cycles and their isochrons (i.e., the sets of points with the same asymptotic phase) for planar vector fields. We formulate a functional equation for the parameterization of the invariant cycle and its isochrons, and we show that it can be solved by means of a Newton method. Using the right transformations, we can solve the equation of the Newton step efficiently. The algorithms are efficient in the sense that if we discretize the functions using ...
Citació
Huguet, G.; de la Llave, R. Computation of limit cycles and their isochrons: Fast algorithms and their convergence. "SIAM journal on applied dynamical systems", 2013, vol. 12, núm. 4, p. 1763-1802.
Paraules clau
biological oscillators, invariant manifolds, isochrons, numerical computation of invariant objects, parameterization method, phase resetting curves
Grup de recerca
SD - Sistemes Dinàmics de la UPC

Participants