The drive-response properties of a system consisting of two identical van der Pol oscillators are investigated. We consider both the coupling constant K and the dissipative coefficient beta as control parameters, and treat the bifurcation between synchronous and asynchronous states as a nonequilibrium phase transition. We investigate in detail the phenomenon of critical slowing-down which occurs as a synchronous phase is driven toward instability. For the limiting case of beta = 0, we find that two linearized oscillators can only be synchronized with appropriate dissipative coupling. The corresponding conditional Lyapunov exponents are calculated, so that the critical slowing-down in synchronous transition at marginal couplings is demonstrated analytically.
