title: Nature of the phase-flip transition in the synchronized approach to amplitude death.
abstract: We study the dynamics of time-delay coupled limit-cycle oscillators in the amplitude death regime. Through a detailed analysis of the Jacobian at the fixed point, we show that the phase-flip transition, namely, the abrupt change from in-phase synchronized dynamics to antiphase synchronized dynamics, is associated with an interchange of the imaginary parts of complex pairs of eigenvalues at an "avoided crossing" of Lyapunov exponents as a parameter is varied. An order parameter for the transition is constructed through the eigenvectors of the Jacobian.
authors.affiliation: School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India.
authors.forename: Rajat
authors.initials: R
authors.lastname: Karnatak
authors.forename: Nirmal
authors.initials: N
authors.lastname: Punetha
authors.forename: Awadhesh
authors.initials: A
authors.lastname: Prasad
authors.forename: Ram
authors.initials: R
authors.lastname: Ramaswamy