title: Bipartite networks of oscillators with distributed delays: Synchronization branches and multistability.
abstract: We study synchronization in bipartite networks of phase oscillators with general nonlinear coupling and distributed time delays. Phase-locked solutions are shown to arise, where the oscillators in each partition are perfectly synchronized among themselves but can have a phase difference with the other partition, with the phase difference necessarily being either zero or π radians. Analytical conditions for the stability of both types of solutions are obtained and solution branches are explicitly calculated, revealing that the network can have several coexisting stable solutions. With increasing value of the mean delay, the system exhibits hysteresis, phase flips, final state sensitivity, and an extreme form of multistability where the numbers of stable in-phase and antiphase synchronous solutions with distinct frequencies grow without bound. The theory is applied to networks of Landau-Stuart and Rössler oscillators and shown to accurately predict both in-phase and antiphase synchronous behavior in appropriate parameter ranges.
authors.affiliation: Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India.
authors.forename: Nirmal
authors.initials: N
authors.lastname: Punetha
authors.affiliation: School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India.|University of Hyderabad, Hyderabad 500 046, India.
authors.forename: Ramakrishna
authors.initials: R
authors.lastname: Ramaswamy
authors.affiliation: Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, Leipzig 04103, Germany.
authors.forename: Fatihcan M
authors.initials: FM
authors.lastname: Atay