This title appears in the Scientific Report : 2007 

TWOFOLD IMPACT OF DELAYED FEEDBACK ON COUPLED OSCILLATORS
Popovych, O. V.
Krachkovskyi, V. / Tass, P. A.
Gehirn & Verhalten; INM-7
International journal of bifurcation and chaos (IJBC), 17 (2007) S. 2517 - 2530
[Singapore] World Scientific 2007
2517 - 2530
10.1142/S0218127407018592
Journal Article
Funktion und Dysfunktion des Nervensystems
International Journal of Bifurcation and Chaos 17
J
Please use the identifier: http://dx.doi.org/10.1142/S0218127407018592 in citations.
We present a detailed bifurcation analysis of desynchronization transitions in a system of two coupled phase oscillators with delay. The coupling between the oscillators combines a delayed self-feedback of each oscillator with an instantaneous mutual interaction. The delayed self-feedback leads to a rich variety of dynamical regimes, ranging from phase-locked and periodically modulated synchronized states to chaotic phase synchronization and desynchronization. We show that an increase of the coupling strength between oscillators may lead to a loss of synchronization. Intriguingly, the delay has a twofold influence on the oscillations: synchronizing for small and intermediate coupling strength and desynchronizing if the coupling strength exceeds a certain threshold value. We show that the desynchronization transition has the form of a crisis bifurcation of a chaotic attractor of chaotic phase synchronization. This study contributes to a better understanding of the impact of time delay on interacting oscillators.