Stochastic Lotkaa-Volterra population dynamics with infinite delay

Fuke Wu; Yong Xu

doi:10.1137/080719194

Stochastic Lotkaa-Volterra population dynamics with infinite delay

Fuke Wu, Yong Xu

Research output: Contribution to journal › Article › Research › peer-review

47 Citations (Scopus)

Abstract

We discover in this paper that when environmental noise is strongly dependent on the population size, this noise may suppress the population explosion in a finite time and guarantee the global positive solution. When the environmental noise is weakly dependent on the population size, the conditions that guarantee the global positive solution are independent of this environmental noise. We also discuss the pth moment boundedness, stochastic ultimate boundedness, and moment average boundedness in time under two classes of conditions. These properties are natural requirements from the biological point of view.

Original language	English
Pages (from-to)	641 - 657
Number of pages	17
Journal	SIAM Journal on Applied Mathematics
Volume	70
Issue number	3
DOIs	https://doi.org/10.1137/080719194
Publication status	Published - 2009
Externally published	Yes

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10.1137/080719194

Cite this

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title = "Stochastic Lotkaa-Volterra population dynamics with infinite delay",

abstract = "We discover in this paper that when environmental noise is strongly dependent on the population size, this noise may suppress the population explosion in a finite time and guarantee the global positive solution. When the environmental noise is weakly dependent on the population size, the conditions that guarantee the global positive solution are independent of this environmental noise. We also discuss the pth moment boundedness, stochastic ultimate boundedness, and moment average boundedness in time under two classes of conditions. These properties are natural requirements from the biological point of view.",

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AB - We discover in this paper that when environmental noise is strongly dependent on the population size, this noise may suppress the population explosion in a finite time and guarantee the global positive solution. When the environmental noise is weakly dependent on the population size, the conditions that guarantee the global positive solution are independent of this environmental noise. We also discuss the pth moment boundedness, stochastic ultimate boundedness, and moment average boundedness in time under two classes of conditions. These properties are natural requirements from the biological point of view.

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DO - 10.1137/080719194

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JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

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