Cross-correlated bounded noises induced the population extinction and enhancement of stability in a population growth model

Abstract

The bounded noises as a new typed non-Gaussian noise have important practical significance. In this paper, the steady state and transient dynamical properties of the population growth model subjected to the cross-correlated sine-Wiener bounded noise are investigated based on the approximate Fokker–Planck Equation. The analytical expressions of stationary probability distribution function and extinction time of the population growth model are obtained. The results show that the bounded noise intensity and the cross-correlated bounded noise intensity can cause the population extinction, in particular, the population density are sensitive to the environmental fluctuation (multiplicative noise) and the self-correlated time. On the other hand, the effects of noise intensities on the extinction time are discussed. The results indicate that the extinction time can be decreased with the intrinsic stochasticity (additive noise) and the self-correlated time increasing. For the positive correlated case, the result is similar to the additive noise and the self-correlated time. However, for the negative correlated case, the extinction time can be increased with the intensity increasing. In particular, the environmental fluctuation (multiplicative noise) causes noise-enhanced stability for the negative correlated case, and the extinction time firstly decreases for the small environmental fluctuation, and then increases for the large environmental fluctuation for the positive correlated case. The numerical results are in basic agreement with the theoretical predictions.