  We study the influence of telegraph noise on synchrony of limit cycle
oscillators. Adopting the phase description for these oscillators, we derive
the explicit expression for the Lyapunov exponent. We show that either for weak
noise or frequent switching the Lyapunov exponent is negative, and the phase
model gives adequate analytical results. In some systems moderate noise can
desynchronize oscillations, and we demonstrate this for the Van der
Pol--Duffing system.
