Long term behavior of solutions of the Lotka-Volterra system under small random perturbations

By Rafail Z. Khasminskii, F. Klebaner. 2001

103 citations recorded by the source corpus.

Subfields: Demography, Global and Planetary Change, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/51316ab03c5d84748a71343da0bb3ef0b219971b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Demography

1. Xiaoyue Li
2. Awad I. El-Gohary
3. A. S. Al-Ruzaiza
4. Chao Zhu
5. Xuerong Mao
6. Fubao Xi
7. Lorens A. Imhof
8. Sotirios Sabanis

In Global and Planetary Change

1. Awad I. El-Gohary
2. A. S. Al-Ruzaiza
3. Chao Zhu
4. Lorens A. Imhof

In Public Health, Environmental and Occupational Health

1. Chao Zhu
2. Xuerong Mao
3. Xiaoyue Li
4. Awad I. El-Gohary
5. A. S. Al-Ruzaiza
6. Lorens A. Imhof
7. Ke Wang
8. Meng Liu

Citations in the corpus

• Chaos and adaptive control in two prey, one predator system with nonlinear feedback (2007, methodology): “A stochastic analysis of the Lotka–Volterra model for the prey–predator when the birth rate of the prey and death rate of the predator are perturbed by independent white noises and others related models are presented in [4], [5], [6], [8], [16], [23] and [28].”
• Jump type stochastic differential equations with non-Lipschitz coefficients: Non-confluence, Feller and strong Feller properties, and exponential ergodicity (2017, background): “For example, in many mathematical ecological models (such as those in Khasminskii and Klebaner (2001), Mao et al. (2002), Zhu and Yin (2009)), the coefficients do not satisfy the linear growth condition; yet non-explosion is still guaranteed thanks to the special structures of the underlying SDEs…”
• Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation (2009, background): “As a matter of fact, stochastic population systems have recently been studied by many authors, for example,[4]-[6], [12]-[14], [20, 23, 25, 26, 30].”
• Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients (2010, unknown): “This is particularly unfortunate as SDEs with superlinearly growing coefficients are quite important in applications (see, e.g., [2, 8, 17, 18, 23, 30, 33]).”
• The long-run behavior of the stochastic replicator dynamics (2005, methodology): “The behavior of solutions to this equation under random perturbations has recently been investigated by Khasminskii and Klebaner (2001), Klebaner and Liptser (2001) and Skorokhod, Hoppensteadt and Salehi [(2002), Section 11].”