The Stochastic stability of a Logistic model with Poisson white noise

Abstract

The stochastic stability of a logistic model subjected to the effect of a random natural environment, modeled as Poisson white noise process, is investigated. The properties of the stochastic response are discussed for calculating the Lyapunov exponent, which had proven to be the most useful diagnostic tool for the stability of dynamical systems. The generalised Itô differentiation formula is used to analyse the stochastic stability of the response. The results indicate that the stability of the response is related to the intensity and amplitude distribution of the environment noise and the growth rate of the species.

Stochastic Dynamics of a Time-Delayed Ecosystem Driven by Poisson White Noise Excitation

“…Therefore, the stochastic jump processes, such as Poisson white noise, are considered to model such pulse-type perturbations [28,29]. So far, studying the stochastic dynamics of ecosystem with stochastic jump process has attracted more and more attention [30][31][32][33][34]. For example, Zhu and his coauthors have investigated the Lotka-Volterra (LV) system under Poisson white noise by using the generalized cell mapping method [32] and the stochastic averaging method [33].…”

“…For example, Zhu and his coauthors have investigated the Lotka-Volterra (LV) system under Poisson white noise by using the generalized cell mapping method [32] and the stochastic averaging method [33]. Duan and Xu have studied the stochastic stability of a logistic model subjected to Poisson white noise process via the Lyapunov exponent [34]. People can find that the influence of Poisson white noise on the ecosystem is different from those of continuous stochastic processes on ecosystem.…”

Mean‐square filtering for polynomial discrete‐time systems with Poisson noises

“…On the other hand, filtering problems usually assume noises of Gaussian type; however, a broad class of random phenomena such as moving loads travelling on a bridge [42], earthquake [43], sea waves and wind actions on ships are modelled as non‐Gaussian random processes [44, 45]. The most common model for non‐Gaussian random processes is Poisson white noise [45].…”

Response of a Duffing—Rayleigh system with a fractional derivative under Gaussian white noise excitation

“…Recently, the response of a nonlinear stochastic system has become a popular topic in theoretical research and engineering practice due to the fact that nonlinear and random phenomena exist widely in nature, society, and engineering. [1][2][3][4] In the last few decades, the fractional derivative has received considerable attention. [5,6] It cannot be denied that the fractional derivative has been used in various scientific and technological fields, [7][8][9][10] such as signal processing, system control, diffusion, edge detection, robotics, biomedicine, turbulence, and viscoelasticity.…”