Most probable trajectories in the delayed tumor growth model excited by a multiplicative non-Gaussian noise

Abstract

This paper investigates the transition phenomenon in the delayed tumor growth model under a multiplicative non-Gaussian colored noise based on the most probable trajectories. Firstly, the unified colored noise approximation and the small delay approximation are utilized to approximate the model in this paper. We then detect the effects of the time-delay, the correlation time and the noise intensity of non-Gaussian colored noise, and find that they can all promote the switch of most probable trajectories from the tumor state to the tumor-free state, namely, the most probable transition time decreases gradually. Conversely, these parameters suppress the transition of most probable trajectories from the tumor-free state to the tumor state, that is, the most probable transition time will increase successively. By analyzing the dynamics under these parameters, it is found that the noise intensity has the greatest influence on the transition behavior. Finally, it can be observed that the sum of the most probable transition time from the tumor-free state to the tumor state and from the tumor state to the tumor-free state is equal to the total observation time.