title: Phase-locked regimes in delay-coupled oscillator networks.
abstract: For an ensemble of globally coupled oscillators with time-delayed interactions, an explicit relation for the frequency of synchronized dynamics corresponding to different phase behaviors is obtained. One class of solutions corresponds to globally synchronized in-phase oscillations. The other class of solutions have mixed phases, and these can be either randomly distributed or can be a splay state, namely with phases distributed uniformly on a circle. In the strong coupling limit and for larger networks, the in-phase synchronized configuration alone remains. Upon variation of the coupling strength or the size of the system, the frequency can change discontinuously, when there is a transition from one class of solutions to another. This can be from the in-phase state to a mixed-phase state, but can also occur between two in-phase configurations of different frequency. Analytical and numerical results are presented for coupled Landau-Stuart oscillators, while numerical results are shown for Rössler and FitzHugh-Nagumo systems.
authors.affiliation: Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India.
authors.forename: Nirmal
authors.initials: N
authors.lastname: Punetha
authors.affiliation: Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India.
authors.forename: Awadhesh
authors.initials: A
authors.lastname: Prasad
authors.affiliation: School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India.
authors.forename: Ramakrishna
authors.initials: R
authors.lastname: Ramaswamy