Time delay and cross-correlated Gaussian noises-induced stochastic stability and regime shift between steady states for an insect outbreak system

Abstract

In this paper, we focus on investigating the stochastic stability and the regime transition between the endangered state and the boom state for a time-delayed insect growth system driven by correlated external and internal noises. By use of the Fokker–Planck equation, the method of small time delay approximation and the fast descent method, we explore in detail the joint action of noise terms and time delay on the mean reproduction and depression time for the insect population. Our investigations indicate that the pseudo-resonance phenomenon of the mean first-passage time (MFPT) occurs because of the impact of different noises and time delay. Through the numerical calculation, it is discovered that multiplicative noise can speed up the shift of the insect population from the boom state to the endangered one, while the noise correlation and time delay can propel the insect system to evolve from the endangered state to the boom state and improve the biological stability. In addition, the impact of the additive noise on the stability of the biological system depends on the positive and negative situation of the noise correlation. On the other hand, during the process of suppressing the insect explosion, it is beneficial to the pest control to amplify the association noise strength and weaken the intensities of the multiplicative, additive noises and time delay. However, during the process of eliminating the pests, it can produce nice effect on the disinsection to increase time delay, the intensities of multiplicative and additive noises and weaken the strength of noise correlation.