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A Stochastic Lotka-Volterra System and Its Asymptotic Behavior

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System Simulation and Scientific Computing (ICSC 2012)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 326))

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Abstract

In this paper, we investigate a new Lotka-Volterra system

$$dx(t)=\textrm{diag}(x_1(t),...,x_n(t))[(b+Ax(t))dt+\sigma x(t)^{p}dw(t))] ,\nonumber $$

where w(t) is a standard Brownian motion, and xp is defined as \((x_{1}^{p},...,x_{n}^{p})^{T}\). Population systems perturbed by the white noise have recently been studied by many authors in case of p = 0 and p = 1. The aim here is to find out what happens when \(p\ge\frac{1}{2}\). This paper shows environmental Brownian noise suppresses explosions in this system. In addition, we examine the asymptotic behavior of the system.

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Donghua University, Shanghai, 201620, P.R. China

    Liangjian Hu & Juanjuan Zhao

Authors
  1. Liangjian Hu
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  2. Juanjuan Zhao
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Editor information

Editors and Affiliations

  1. National CIMS Engineering Research Center, Department of Automation, Tsinghua University, 100084, Beijing, China

    Tianyuan Xiao

  2. School of Automation Science and Electrical Engineering, Beihang University, 100191, Beijing, China

    Lin Zhang

  3. School of Mechatronics Engineering and Automation, Shanghai University, 200072, Shanghai, China

    Shiwei Ma

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Hu, L., Zhao, J. (2012). A Stochastic Lotka-Volterra System and Its Asymptotic Behavior. In: Xiao, T., Zhang, L., Ma, S. (eds) System Simulation and Scientific Computing. ICSC 2012. Communications in Computer and Information Science, vol 326. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34381-0_51

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  • DOI: https://doi.org/10.1007/978-3-642-34381-0_51

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34380-3

  • Online ISBN: 978-3-642-34381-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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