title: Phase-flip transition in relay-coupled nonlinear oscillators.
abstract: We study the dynamics of oscillators that are coupled in relay; namely, through an intermediary oscillator. From previous studies it is known that the oscillators show a transition from in-phase to out-of-phase oscillations or vice versa when the interactions involve a time delay. Here we show that, in the absence of time delay, relay coupling through conjugate variables has the same effect. However, this phase-flip transition does not occur abruptly at a certain critical value of the coupling parameter. Instead we find a parameter region around the phase-flip transition where bistability occurs. In this parameter interval in-phase and out-of-phase oscillations coexist with changing sizes of their basins of attraction. Further increase of the coupling strength leads to amplitude death and subsequently to the stabilization of a fixed point. These transitions are characterized through various quantities such as the average phase difference and crossings in the spectrum of Lyapunov exponents. Numerical results are presented for a specific case of coupled Rössler-like oscillators.
authors.affiliation: The LNM Institute of Information Technology, Jaipur, India.
authors.forename: Amit
authors.initials: A
authors.lastname: Sharma
authors.forename: Manish Dev
authors.initials: MD
authors.lastname: Shrimali
authors.forename: Awadhesh
authors.initials: A
authors.lastname: Prasad
authors.forename: Ram
authors.initials: R
authors.lastname: Ramaswamy
authors.forename: Ulrike
authors.initials: U
authors.lastname: Feudel