Lévy noise-induced transition and stochastic resonance in a tumor growth model

Abstract

The stationary probability density and stochastic resonance phenomenon of a tumor growth model under the excitation of Lévy noise and Gaussian white noise are investigated in this paper. The fourth-order Runge-Kutta method and the Janick-Weron algorithm are used to simulate the stationary probability density. Meanwhile, the signal-to-noise ratio(SNR) is studied as a function of Lévy noise intensity and Gaussian white noise intensity by numerical simulation respectively. The results indicate that: (i)both Lévy and Gaussian noise sources give rise to noise-induced transitions for the system, with a peculiarity that smaller stability indexα and Lévy noise intensity D enhance the likelihood of tumor cell death; (ii)both noise parameters and system parameters can induce the occurrence of stochastic resonance. However, the effect of Gaussian white noise on SNR is different from that of Lévy noise.