Dynamics of a stochastic Lotka–Volterra model perturbed by white noise
By N. Du, V. H. Sam. 2006
108 citations recorded by the source corpus.
Abstract This paper continues the study of Mao et al. investigating two aspects of the equation d x ( t ) = diag ( x 1 ( t ) , … , x n ( t ) ) [ ( b + A x ( t ) ) d t + σ x ( t ) d W ( t ) ] , t ⩾ 0 . The first of these is to slightly improve results in [X. Mao, S. Sabais, E. Renshaw, Asymptotic behavior of stochastic Lotka–Volterra model, J. Math. Anal. 287 (2003) 141–156] concerning with the upper-growth rate of the total quantity ∑ i = 1 n x i ( t ) of species by weakening hypotheses posed on the coefficients of the equation. The second aspect is to investigate the lower-growth rate of the positive solutions. By using Lyapunov function technique and using a changing time method, we prove that the total quantity ∑ i = 1 n x i ( t ) always visits any neighborhood of the point 0 and we simultaneously give estimates for this lower-growth rate.
Subfields: Genetics, Public Health, Environmental and Occupational Health, Sociology and Political Science
View Paper: https://www.semanticscholar.org/paper/ae295498c5e5fe762bf93326ae58c87222144b9e
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Citations in the corpus
- Stochastic Lotka–Volterra systems with Lévy noise (2014, unknown): “[2,6–8,10,12,14–17,19–21]).”
- Persistence and extinction in stochastic non-autonomous logistic systems (2011, unknown): “The studies [9–13] are the former type while the investigations [14–23] are the latter case.”
- On competitive Lotka-Volterra model in random environments (2009, methodology): “One of the main results in [32] is that the environmental noise can suppress a potential population explosion; see also [8,31] among others in this connection.”
- Coexistence and exclusion of stochastic competitive Lotka–Volterra models (2016, background): “General Lotka-Volterra models perturbed by white noise have been studied in [6, 11, 14, 16, 17], while the authors in [21, 26, 31, 32] go further by considering the effect of both white and colored noises to the Lotka-Volterra models.”