Geodesic
Isochronous bifurcations in second-order delay differential equations
Electronic journal of differential equations, Tome 2014 (2014)
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__a29,
     author = {Bel,  Andrea and Reartes,  Walter},
     title = {Isochronous bifurcations in second-order delay differential equations},
     journal = {Electronic journal of differential equations},
     year = {2014},
     volume = {2014},
     zbl = {1300.34155},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a29/}
}
TY  - JOUR
AU  - Bel,  Andrea
AU  - Reartes,  Walter
TI  - Isochronous bifurcations in second-order delay differential equations
JO  - Electronic journal of differential equations
PY  - 2014
VL  - 2014
UR  - http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a29/
LA  - en
ID  - EJDE_2014__2014__a29
ER  - 
%0 Journal Article
%A Bel,  Andrea
%A Reartes,  Walter
%T Isochronous bifurcations in second-order delay differential equations
%J Electronic journal of differential equations
%D 2014
%V 2014
%U http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a29/
%G en
%F EJDE_2014__2014__a29
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__a29/