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Mean exit time and escape probability for the stochastic logistic growth model with multiplicative α-stable Lévy noise
Stochastics and Dynamics  (IF0.98),  Pub Date : 2020-08-28, DOI: 10.1142/s0219493721500167
Almaz Tesfay, Daniel Tesfay, Anas Khalaf, James Brannan

In this paper, we formulate a stochastic logistic fish growth model driven by both white noise and non-Gaussian noise. We focus our study on the mean time to extinction, escape probability to measure the noise-induced extinction probability and the Fokker–Planck equation for fish population X(t). In the Gaussian case, these quantities satisfy local partial differential equations while in the non-Gaussian case, they satisfy nonlocal partial differential equations. Following a discussion of existence, uniqueness and stability, we calculate numerical approximations of the solutions of those equations. For each noise model we then compare the behaviors of the mean time to extinction and the solution of the Fokker–Planck equation as growth rate r, carrying capacity K, intensity of Gaussian noise λ, noise intensity σ and stability index α vary. The MET from the interval (0,1) at the right boundary is finite if λ<2. For λ>2, the MET from (0,1) at this boundary is infinite. A larger stability index α is less likely leading to the extinction of the fish population.