Stochastic dynamical features for a time-delayed ecological system of vegetation subjected to correlated multiplicative and additive noises

In this paper, the generalized potential function, the stationary probability distribution function (SPDF), the mean development time and the mean shrinking time of a time-delayed vegetation growth system induced by cross-correlated internal and external noises are investigated. Our main results are designed to reveal the fact that the resonant phenomenon of the mean first-passage time (MFPT) takes place in the vegetation growth model because of the interaction of different types of noises and time delay. It can inhibit the vegetation system from developing rapidly and reduce the stability of the system by increasing of intensity of multiplicative noise and time delay. Meanwhile, it can produce beneficial effect on maintaining the stability of the vegetation system by increasing the strength of correlated noise. However, it can exert complicated effect on the stability of system by increasing the intensity of additive noise in different cases. During the spread process of the vegetation, it plays a positive role in propelling the development of vegetation by reducing the cross-correlated noise strength and increasing the multiplicative, additive noise intensities and time delay. On the contrary, in the decline process of vegetation system, it plays a crucial part in maintaining the vegetation biomass by increasing the strength of cross-correlated noise and weaken the multiplicative, additive noise intensities and time delay.