Electron. J. Diff. Equ., Vol. 2014 (2014), No. 162, pp. 1-12.

Isochronous bifurcations in second-order delay differential equations

Andrea Bel, Walter Reartes

Abstract:
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.

Submitted November 4, 2013. Published July 24, 2014.
Math Subject Classifications: 34K13, 34K18
Key Words: Delay differential equations; Hopf bifurcation; isochronous cycles.

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Andrea Bel
Universidad Nacional del Sur
Av. Alem 1253, 8000 Bahía Blanca
Buenos Aires, Argentina
email: andrea.bel@uns.edu.ar
Walter Reartes
Universidad Nacional del Sur
Av. Alem 1253, 8000 Bahía Blanca
Buenos Aires, Argentina
email: walter.reartes@gmail.com

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