Global stability and stochastic permanence of a non-autonomous logistic equation with random perturbation☆

By Daqing Jiang, N. Shi, Xiaoyue Li. 2008

225 citations recorded by the source corpus.

Abstract This paper discusses a randomized non-autonomous logistic equation d N ( t ) = N ( t ) [ ( a ( t ) − b ( t ) N ( t ) ) d t + α ( t ) d B ( t ) ] , where B ( t ) is a 1-dimensional standard Brownian motion. In [D.Q. Jiang, N.Z. Shi, A note on non-autonomous logistic equation with random perturbation, J. Math. Anal. Appl. 303 (2005) 164–172], the authors show that E [ 1 / N ( t ) ] has a unique positive T -periodic solution E [ 1 / N p ( t ) ] provided a ( t ) , b ( t ) and α ( t ) are continuous T -periodic functions, a ( t ) > 0 , b ( t ) > 0 and ∫ 0 T [ a ( s ) − α 2 ( s ) ] d s > 0 . We show that this equation is stochastically permanent and the solution N p ( t ) is globally attractive provided a ( t ) , b ( t ) and α ( t ) are continuous T -periodic functions, a ( t ) > 0 , b ( t ) > 0 and min t ∈ [ 0 , T ] a ( t ) > max t ∈ [ 0 , T ] α 2 ( t ) . By the way, the similar results of a generalized non-autonomous logistic equation with random perturbation are yielded.

Subfields: Applied Mathematics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/170fcdf8874fd3eb8c8c4595a626f41c5ebc40dc

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In Applied Mathematics

1. Xiaoyue Li
2. Xuerong Mao
3. Chenggui Yuan

In Modeling and Simulation

1. Xuerong Mao
2. Xiaoyue Li
3. Ke Wang
4. Meng Liu

In Public Health, Environmental and Occupational Health

1. Xuerong Mao
2. Xiaoyue Li
3. Ke Wang
4. Meng Liu
5. Chenggui Yuan

Citations in the corpus

• 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.”
• Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation (2009, background): “This corollary is one of the main results in [11].”
• Sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic populations under regime switching (2011, background): “In [6], the authors considered a more complicated case corresponding to (1.”
• Population dynamical behavior of Lotka-Volterra cooperative systems with random perturbations (2012, unknown): “[16, 20, 21, 22, 24, 25]) Eq.”