Geodesic
Isochronous bifurcations in second-order delay differential equations
Electronic Journal of Differential Equations, Tome 2014 (2014).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this article we consider a special type of second-order delay differential equations. More precisely, we take an equation of a conservative mechanical system in one dimension with an added term that is a function of the difference between the value of the position at time t minus the position at the delayed time $t-\tau$. For this system, we show that, under certain conditions of non-degeneration and of convergence of the periodic solutions obtained by the Homotopy Analysis Method, bifurcation branches appearing in a neighbourhood of Hopf bifurcation due to the delay are isochronous; i.e., all the emerging cycles have the same frequency.
Classification : 34K13, 34K18
Keywords: delay differential equations, Hopf bifurcation, isochronous cycles 
@article{EJDE_2014__2014__a129,
     author = {Bel, Andrea and Reartes, Walter},
     title = {Isochronous bifurcations in second-order delay differential equations},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2014},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a129/}
}
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Bel, Andrea; Reartes, Walter. Isochronous bifurcations in second-order delay differential equations. Electronic Journal of Differential Equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a129/