Stochastic dynamical characteristics for a time-delayed insect outbreak model driven by correlated multiplicative and additive noises

In this paper, we numerically investigate the stability and transient properties of an insect outbreak model driven by correlated multiplicative, additive Gaussian noises and time delay. By using the Fokker-Planck equation, the small time delay method and the fast descent method, we analyze the mean reproduction and decline time of the insect growth system. Numerical results show that the resonant phenomenon of maximization of the mean first-passage time (MFPT) appears due to the joint action of all kinds of noises and time delay. It can hold down the insect population transfer from the stable state of a small number to the large one, enhance effectively the stability of the system and further inhibit the expansion of the insect population to increase noises intensities and time delay. In the process of restraining the expansion of the insect population, the increase of the association noise strength caused by the intrinsic noise and the extrinsic noise, and time delay make a beneficial contribution to restraining the outbreak of the insect population. Analogously, the appropriate multiplicative and additive noise intensities can play a positive role in the inhibition of pests. On the contrary, during the process of destroying a large number of insects, the increase of all noises and time delay can produce positive effects on controlling a plague of insects.