Time delay and non-Gaussian noise-enhanced stability of foraging colony system

Abstract

In view of the role of external noise, the statistical characteristics of foraging colony system with non-Gaussian noise and time delay are investigated. By means of the small time delay approximation and the Markov approximation, the expressions of stationary probability distribution and mean first passage time (MFPT) of foraging colony system are derived. Using the stochastic second-order Runge–Kutta algorithm, the stationary probability distribution of system, MFPT from the metastable state to stable state, and the probability density function (PDF) of the first passage time from the metastable state to stable state are stimulated. The results show that: (i) the external noise intensity α and the parameter q of departure from Gaussian noise can induce transition phenomenon; (ii) the MFPT as a function of α shows a minimum, which is enhanced by internal noise; (iii) the external noise can enhance stability of system; (iv) time delay-enhanced stability of system occurs.