Stochastic delayed kinetics of foraging colony system under non-Gaussian noise

Abstract

In this paper, the stochastic kinetics in a time-delayed foraging colony system under non-Gaussian noise were investigated. Using delay Fokker–Planck approach, the stationary probability distribution (SPD), the normalized variance β2, skewness β3 and kurtosis β4 of the state variable are obtained, respectively. The effects of the time delayed feedback and non-Gaussian noise on the SPD are analyzed theoretically. The numerical simulations about the SPD are obtained and in good agreement with the approximate theoretical results. Furthermore, the impacts of the time delayed feedback and non-Gaussian noise on the β2, β3 and β4 are discussed, respectively. It is found that the curves in β2, β3 and β4 exhibit an optimum strength of feedback where β2, β3 and β4 have a maximum. This maximum indicates the large deviations in β2, β3 and β4. From the above findings, it is easy for us to have a further understanding of the roles of the time delayed feedback and non-Gaussian noise in the foraging colonies system.