Mean extinction time and stability for a metapopulation system subjected to correlated Gaussian and non-Gaussian noises

• A stochastic model for the metapopulation system including non-Gaussian and Gaussian noises is established.
• The generalized potential function of the metapopulation system under a correlated non-Gaussian multiplicative noise and a Gaussian additive noise is studied.
• The mean extinction time of the metapopulation system driven by a non-Gaussian noise and a Gaussian additive noise is discussed.

In this paper, we investigate the shift between the stable state of a large density and the extinction state, the mean extinction time for a metapopulation system induced by the associated Gaussian additive noise and non-Gaussian multiplicative noise. By applying the approximate Fokker–Planck equation, the fast descent method and the path integral approach, we obtain the expressions of the effective potential function and the mean extinction time. The numerical results show that the additive noise can damage the stability of the system, while the associated noise and the noise correlation times τ0τ0 and ττ can strengthen the stability of the population system. In the meantime, the maximum of the mean first-passage time appears in the meta-population system due to the impacts of different types of noises and their correlation time terms. It can effectively extend the extinction time of the metapopulation to enhance the strength of the correlation noise and two terms of noise correlation time. Conversely, the additive noise plays a negative role in preventing the extinction of the population. On the other side, a proper small multiplicative noise intensity can produce the positive effect on lengthening the life of the metapopulation.