Lévy noise-induced transition and stochastic resonance in Brusselator system

The noise-induced transition and stochastic resonance (SR) phenomenon of Brusselator system under the excitation of Lévy noise is investigated in this paper. The Janicki–Weron algorithm is used to simulate Lévy noise, and the stationary probability density is obtained by solving the system equation through the fourth-order stochastic Runge–Kutta algorithm. The influences of the noise intensity, stability index and skewness parameter on the stationary probability density are analyzed. The numerical results imply that the stability index, skewness parameter and noise intensity can induce the transition. Moreover, the effects of the stability index and skewness parameter of Lévy noise, as well as the amplitude of external signal on the signal-to-noise ratio are discussed. The research results show that the larger stability index, skewness parameter and signal amplitude are beneficial to the occurrence of SR.