Gaussian and Lévy noises excited delayed tumor growth model: first-passage behavior and stochastic resonance

Abstract

In this paper, we analyze the dynamical behavior of a delayed tumor growth model under the joint effect of Gaussian white noise and Lévy noise by studying the mean first passage time (MFPT) and stochastic resonance (SR). Firstly, the tumor growth model under the joint effect of Gaussian white noise, Lévy noise and time delay is introduced. Then, the Lévy noise sequence is simulated by Janicki-Weron algorithm, and the MFPT and signal-to-noise ratio(SNR) of the system are simulated by using fourth-order stochastic Runge-Kutta algorithm. The effects of noise parameters, time delay and periodic signal parameters on MFPT, SR are discussed in detail, respectively. In addition, we find the phenomenon of noise enhanced stability. The results of the study can help to select the optimal regulatory parameters in the tumor growth model and promote the treatment of tumors.