The Stationary Distribution of Competitive Lotka-Volterra Population Systems with Jumps

Dynamics of Lotka-Volterra population with jumps (LVWJ) have recently been established (see Bao et al., 2011, and Bao and Yuan, 2012). They provided some useful criteria on the existence of stationary distribution and some asymptotic properties for LVWJ. However, the uniqueness of stationary distrib...

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Main Authors: Zhenzhong Zhang, Jinying Tong, Jianhai Bao
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/820831
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author Zhenzhong Zhang
Jinying Tong
Jianhai Bao
author_facet Zhenzhong Zhang
Jinying Tong
Jianhai Bao
author_sort Zhenzhong Zhang
collection DOAJ
description Dynamics of Lotka-Volterra population with jumps (LVWJ) have recently been established (see Bao et al., 2011, and Bao and Yuan, 2012). They provided some useful criteria on the existence of stationary distribution and some asymptotic properties for LVWJ. However, the uniqueness of stationary distribution for n≥2 and asymptotic pathwise estimation limt→+∞⁡(1/t)∫0t‍|X(s)|pds (p>0) are still unknown for LVWJ. One of our aims in this paper is to show the uniqueness of stationary distribution and asymptotic pathwise estimation for LVWJ. Moreover, some characterizations for stationary distribution are provided.
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spelling doaj-art-1e45c3061cf148e1882e6b2c7ffb1d312025-08-20T02:04:44ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/820831820831The Stationary Distribution of Competitive Lotka-Volterra Population Systems with JumpsZhenzhong Zhang0Jinying Tong1Jianhai Bao2College of Science, Donghua University, Shanghai 201620, ChinaCollege of Science, Donghua University, Shanghai 201620, ChinaDepartment of Mathematics, Central South University, Changsha 410075, ChinaDynamics of Lotka-Volterra population with jumps (LVWJ) have recently been established (see Bao et al., 2011, and Bao and Yuan, 2012). They provided some useful criteria on the existence of stationary distribution and some asymptotic properties for LVWJ. However, the uniqueness of stationary distribution for n≥2 and asymptotic pathwise estimation limt→+∞⁡(1/t)∫0t‍|X(s)|pds (p>0) are still unknown for LVWJ. One of our aims in this paper is to show the uniqueness of stationary distribution and asymptotic pathwise estimation for LVWJ. Moreover, some characterizations for stationary distribution are provided.http://dx.doi.org/10.1155/2014/820831
spellingShingle Zhenzhong Zhang
Jinying Tong
Jianhai Bao
The Stationary Distribution of Competitive Lotka-Volterra Population Systems with Jumps
Abstract and Applied Analysis
title The Stationary Distribution of Competitive Lotka-Volterra Population Systems with Jumps
title_full The Stationary Distribution of Competitive Lotka-Volterra Population Systems with Jumps
title_fullStr The Stationary Distribution of Competitive Lotka-Volterra Population Systems with Jumps
title_full_unstemmed The Stationary Distribution of Competitive Lotka-Volterra Population Systems with Jumps
title_short The Stationary Distribution of Competitive Lotka-Volterra Population Systems with Jumps
title_sort stationary distribution of competitive lotka volterra population systems with jumps
url http://dx.doi.org/10.1155/2014/820831
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