Population dynamical behavior of Lotka–Volterra system under regime switching

Li, Xiaoyue; Jiang, Daqing; Mao, Xuerong

doi:10.1016/j.cam.2009.06.021

Cited by 154 publications

(103 citation statements)

References 24 publications

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Section: (T) (T) (T) (T) (T) (T) (T)mentioning

confidence: 99%

“…In fact, population system is often subject to effect by environmental noise (see [1][2][3]). In paper [2][3], some result on the nonexplosion, boundedness and persistence for stochastic population systems have been developed. Particularly, Ji and Jiang in [3] studied nonautonomous two-species stochastic Lotka-Volterra mutualism model     (2) For the systems (2) and its generalized forms, many interesting results have been obtained.…”

Section: (T) (T) (T) (T) (T) (T) (T)mentioning

confidence: 99%

“…In paper [2][3], some result on the nonexplosion, boundedness and persistence for stochastic population systems have been developed. Particularly, Ji and Jiang in [3] studied nonautonomous two-species stochastic Lotka-Volterra mutualism model     (2) For the systems (2) and its generalized forms, many interesting results have been obtained. On the other hand, the growth of species usually undergoes some discrete changes of relatively short time interval at some fixed times, such as drought, flooding, earthquake, planting, harvesting etc.…”

Section: (T) (T) (T) (T) (T) (T) (T)mentioning

confidence: 99%

“…From point view of mathematic, the sudden changes could be described by impulses. In this case, impulsive effects should be taken into account system (2). Some results (see [4][5][6][7]) have been proposed for stochastic systems with impulsive effects.…”

Section: (T) (T) (T) (T) (T) (T) (T)mentioning

confidence: 99%

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Stochastic Non-autonomous Lotka-Volterra Mutualism systems with Impulse Jump and Markov Switching

Lu¹,

Zhang²

2016

Proceedings of the 2016 International Conference on Artificial Intelligence and Engineering Applications

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Section: (T) (T) (T) (T) (T) (T) (T)mentioning

confidence: 99%

Section: (T) (T) (T) (T) (T) (T) (T)mentioning

confidence: 99%

Section: (T) (T) (T) (T) (T) (T) (T)mentioning

confidence: 99%

Section: (T) (T) (T) (T) (T) (T) (T)mentioning

confidence: 99%

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Stochastic Non-autonomous Lotka-Volterra Mutualism systems with Impulse Jump and Markov Switching

Lu¹,

Zhang²

2016

Proceedings of the 2016 International Conference on Artificial Intelligence and Engineering Applications

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“…However, due to the complexity of the process in nature, population systems are often subject to environmental noise, which is an important component in the real ecosystem. A system with such random perturbations tends to be suitably modelled by stochastic differential equations [12,17,37]. Nisbet and Gurney [22] demonstrated that stochastic differential equations models play a significant role in the analysis of various dynamic systems, because they can provide an additional degree of realism compared to their deterministic counterpart.…”

Section: Introductionmentioning

confidence: 99%

The stochastic interactions between predator and prey under Markovian switching: competitive interaction between multiple prey

Li¹,

Zhang²

2017

J. Nonlinear Sci. Appl.

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In this paper, a class of predator-prey model with prey competition is proposed, in which the interactions of predation between predator and prey are randomised and subsequently evaluated under Markovian switching. By constructing appropriate Lyapunov functions and applying various analytical methods, sufficient conditions for the existence of unique global positive solution, stochastic permanence and mean extinction are established. In the permanence case, we also estimate the superior and inferior limits of the sample path in a time-averaged Markov decision. We conclude that the interactions between predator and two prey, two competitive prey themselves and the dynamical properties of switching subsystems are not only dependent on subsystem coefficients but also on the transition probability of the Markov chain (switching from one state to another). Specific examples and numerical simulations are provided to demonstrate our theoretical results.

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The protection zone for biological population in random environment

Zou

2012

Math Methods in App Sciences

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A biomathematical model is described by stochastic differential equations with Markovian switching. The long‐time dynamical properties are studied both theoretically and numerically. Results show that both the persistence and extinction have close relationship with environmental noises (white and color noises). These results are of important biological significance for biological conservation. Copyright © 2012 John Wiley & Sons, Ltd.

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Population dynamical behavior of Lotka–Volterra system under regime switching

Cited by 154 publications

References 24 publications

Stochastic Non-autonomous Lotka-Volterra Mutualism systems with Impulse Jump and Markov Switching

Stochastic Non-autonomous Lotka-Volterra Mutualism systems with Impulse Jump and Markov Switching

The stochastic interactions between predator and prey under Markovian switching: competitive interaction between multiple prey

The protection zone for biological population in random environment

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