Suppression of Oscillations by Lévy Noise

We find the analytic solution of a pair of stochastic equations with arbitrary forces and multiplicative Lévy noises in a steady-state nonequilibrium case. This solution shows that Lévy flights always suppress a quasiperiodic motion related to the limit cycle. We prove that such suppression is caused by that the Lévy variation ∆L ~ (∆t)1/α with the exponent α < 2 is always negligible in comparison with the Gaussian variation ∆W ~ (∆t)1/2 in the ∆t → 0 limit.