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Volumn 23, Issue 5, 2013, Pages 751-775

Dynamics of a two-prey one-predator system in random environments

Author keywords

Extinction; Global asymptotic stability; Random perturbations; Stationary distribution; Two prey one predator model

Indexed keywords

ERGODIC PROPERTY; GLOBAL ASYMPTOTIC STABILITY; POSITIVE CONSTANT; POSITIVE SOLUTION; RANDOM ENVIRONMENT; RANDOM PERTURBATIONS; STATIONARY DISTRIBUTION; TWO-PREY ONE-PREDATOR SYSTEM;

EID: 84884672931     PISSN: 09388974     EISSN: 14321467     Source Type: Journal    
DOI: 10.1007/s00332-013-9167-4     Document Type: Article
Times cited : (96)

References (32)
  • 1
    • 0034172677 scopus 로고    scopus 로고
    • Average conditions for global asymptotic stability in a nonautonomous Lotka-Volterra system
    • 1768401 10.1016/S0362-546X(00)85003-8
    • Ahmad, S., Lazer, A.C.: Average conditions for global asymptotic stability in a nonautonomous Lotka-Volterra system. Nonlinear Anal. 40, 37-49 (2000)
    • (2000) Nonlinear Anal. , vol.40 , pp. 37-49
    • Ahmad, S.1    Lazer, A.C.2
  • 2
    • 0041573427 scopus 로고    scopus 로고
    • Almost necessary and sufficient conditions for survival of species
    • 2004095 10.1016/S1468-1218(03)00037-3
    • Ahmad, S., Stamova, I.M.: Almost necessary and sufficient conditions for survival of species. Nonlinear Anal. 5, 219-229 (2004)
    • (2004) Nonlinear Anal. , vol.5 , pp. 219-229
    • Ahmad, S.1    Stamova, I.M.2
  • 3
    • 24344490836 scopus 로고    scopus 로고
    • Stochastic delay population dynamics
    • 2039641
    • Bahar, A., Mao, X.: Stochastic delay population dynamics. Int. J. Pure Appl. Math. 11, 377-400 (2004)
    • (2004) Int. J. Pure Appl. Math. , vol.11 , pp. 377-400
    • Bahar, A.1    Mao, X.2
  • 4
    • 0001274382 scopus 로고
    • Systems d'equations differentielles d'oscillations nonlineaires
    • 111896
    • Barbalat, I.: Systems d'equations differentielles d'oscillations nonlineaires. Rev. Roum. Math. Pures Appl. 4, 267-270 (1959)
    • (1959) Rev. Roum. Math. Pures Appl. , vol.4 , pp. 267-270
    • Barbalat, I.1
  • 5
    • 0000735971 scopus 로고
    • Harvesting natural populations in a randomly fluctuating environment
    • 10.1126/science.197.4302.463
    • Beddington, J.R., May, R.M.: Harvesting natural populations in a randomly fluctuating environment. Science 197, 463-465 (1977)
    • (1977) Science , vol.197 , pp. 463-465
    • Beddington, J.R.1    May, R.M.2
  • 6
    • 33847329574 scopus 로고    scopus 로고
    • Itô versus Stratonovich calculus in random population growth
    • 2311673 10.1016/j.mbs.2004.09.002
    • Braumann, C.A.: Itô versus Stratonovich calculus in random population growth. Math. Biosci. 206, 81-107 (2007)
    • (2007) Math. Biosci. , vol.206 , pp. 81-107
    • Braumann, C.A.1
  • 8
    • 70449568737 scopus 로고    scopus 로고
    • Stochastic population systems
    • 2541380 10.1080/07362990902844348
    • Cheng, S.: Stochastic population systems. Stoch. Anal. Appl. 27, 854-874 (2009)
    • (2009) Stoch. Anal. Appl. , vol.27 , pp. 854-874
    • Cheng, S.1
  • 9
    • 38248999812 scopus 로고
    • Coexistence, stability, and limiting behavior in a one-predator-two-prey model
    • 1249840 10.1006/jmaa.1993.1371
    • Feng, W.: Coexistence, stability, and limiting behavior in a one-predator-two-prey model. J. Math. Anal. Appl. 179, 592-609 (1993)
    • (1993) J. Math. Anal. Appl. , vol.179 , pp. 592-609
    • Feng, W.1
  • 10
    • 0017407813 scopus 로고
    • Mathematical analysis of some three-species food-chain models
    • 682262 10.1016/0025-5564(77)90142-0
    • Freedman, H., Waltman, P.: Mathematical analysis of some three-species food-chain models. Math. Biosci. 33, 257-276 (1977)
    • (1977) Math. Biosci. , vol.33 , pp. 257-276
    • Freedman, H.1    Waltman, P.2
  • 11
    • 48749138514 scopus 로고
    • Persistence in models of three interacting predator-prey populations
    • 738903 10.1016/0025-5564(84)90032-4
    • Freedman, H., Waltman, P.: Persistence in models of three interacting predator-prey populations. Math. Biosci. 68, 213-231 (1984)
    • (1984) Math. Biosci. , vol.68 , pp. 213-231
    • Freedman, H.1    Waltman, P.2
  • 14
    • 0035439412 scopus 로고    scopus 로고
    • An algorithmic introduction to numerical simulation of stochastic differential equations
    • 1872387 10.1137/S0036144500378302
    • Higham, D.: An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM Rev. 43, 525-546 (2001)
    • (2001) SIAM Rev. , vol.43 , pp. 525-546
    • Higham, D.1
  • 15
    • 80051793603 scopus 로고    scopus 로고
    • The estimation of probability distribution of SDE by only one sample trajectory
    • 2834166 10.1016/j.camwa.2011.06.023
    • Hu, G., Wang, K.: The estimation of probability distribution of SDE by only one sample trajectory. Comput. Math. Appl. 62, 1798-1806 (2011)
    • (2011) Comput. Math. Appl. , vol.62 , pp. 1798-1806
    • Hu, G.1    Wang, K.2
  • 16
    • 0020736663 scopus 로고
    • A criterion for permanent co-existence of species, with an application to a two-prey one-predator system
    • 695730 10.1016/0025-5564(82)90042-6
    • Hutson, V., Vickers, G.: A criterion for permanent co-existence of species, with an application to a two-prey one-predator system. Math. Biosci. 63, 253-269 (1983)
    • (1983) Math. Biosci. , vol.63 , pp. 253-269
    • Hutson, V.1    Vickers, G.2
  • 17
    • 37449001667 scopus 로고    scopus 로고
    • Global stability and stochastic permanence of a non-autonomous logistic equation with random perturbation
    • 2376180 10.1016/j.jmaa.2007.08.014
    • Jiang, D., Shi, N., Li, X.: Global stability and stochastic permanence of a non-autonomous logistic equation with random perturbation. J. Math. Anal. Appl. 340, 588-597 (2008)
    • (2008) J. Math. Anal. Appl. , vol.340 , pp. 588-597
    • Jiang, D.1    Shi, N.2    Li, X.3
  • 18
    • 84862797638 scopus 로고    scopus 로고
    • Analysis of autonomous Lotka-Volterra competition systems with random perturbation
    • 2890539 10.1016/j.jmaa.2011.12.049
    • Jiang, D., Ji, C., Li, X., O'Regan, D.: Analysis of autonomous Lotka-Volterra competition systems with random perturbation. J. Math. Anal. Appl. 390, 582-595 (2012)
    • (2012) J. Math. Anal. Appl. , vol.390 , pp. 582-595
    • Jiang, D.1    Ji, C.2    Li, X.3    O'Regan, D.4
  • 20
    • 67650711514 scopus 로고    scopus 로고
    • Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation
    • 2486589 10.3934/dcds.2009.24.523
    • Li, X., Mao, X.: Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation. Discrete Contin. Dyn. Syst. 24, 523-545 (2009)
    • (2009) Discrete Contin. Dyn. Syst. , vol.24 , pp. 523-545
    • Li, X.1    Mao, X.2
  • 21
    • 78650055169 scopus 로고    scopus 로고
    • Sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic populations under regime switching
    • 2745384 10.1016/j.jmaa.2010.10.053
    • Li, X., Gray, A., Jiang, D., Mao, X.: Sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic populations under regime switching. J. Math. Anal. Appl. 376, 11-28 (2011)
    • (2011) J. Math. Anal. Appl. , vol.376 , pp. 11-28
    • Li, X.1    Gray, A.2    Jiang, D.3    Mao, X.4
  • 22
    • 79960381828 scopus 로고    scopus 로고
    • Survival analysis of a stochastic cooperation system in a polluted environment
    • 10.1142/S0218339011003877
    • Liu, M., Wang, K.: Survival analysis of a stochastic cooperation system in a polluted environment. J. Biol. Syst. 19, 183-204 (2011)
    • (2011) J. Biol. Syst. , vol.19 , pp. 183-204
    • Liu, M.1    Wang, K.2
  • 23
    • 79961026130 scopus 로고    scopus 로고
    • Survival analysis of stochastic competitive models in a polluted environment and stochastic competitive exclusion principle
    • 2823174 10.1007/s11538-010-9569-5
    • Liu, M., Wang, K., Wu, Q.: Survival analysis of stochastic competitive models in a polluted environment and stochastic competitive exclusion principle. Bull. Math. Biol. 73, 1969-2012 (2011)
    • (2011) Bull. Math. Biol. , vol.73 , pp. 1969-2012
    • Liu, M.1    Wang, K.2    Wu, Q.3
  • 24
    • 62549127716 scopus 로고    scopus 로고
    • Stochastic population dynamics under regime switching II
    • 2521735 10.1016/j.jmaa.2009.02.010
    • Luo, Q., Mao, X.: Stochastic population dynamics under regime switching II. J. Math. Anal. Appl. 355, 577-593 (2009)
    • (2009) J. Math. Anal. Appl. , vol.355 , pp. 577-593
    • Luo, Q.1    Mao, X.2
  • 26
    • 84884675025 scopus 로고
    • Stochastic three species systems
    • 1069012 10.1007/BF00164165
    • Sridhara, R., Watson, R.: Stochastic three species systems. J. Math. Biol. 28, 595-607 (1990)
    • (1990) J. Math. Biol. , vol.28 , pp. 595-607
    • Sridhara, R.1    Watson, R.2
  • 28
    • 0001342110 scopus 로고
    • Existence of bifurcation of stable equilibrium in two-prey, one-predator communities
    • 727352
    • Takeuchi, Y., Adachi, N.: Existence of bifurcation of stable equilibrium in two-prey, one-predator communities. Bull. Math. Biol. 45, 877-900 (1983)
    • (1983) Bull. Math. Biol. , vol.45 , pp. 877-900
    • Takeuchi, Y.1    Adachi, N.2
  • 29
    • 70350337336 scopus 로고    scopus 로고
    • Survival of three species in a nonautonomous Lotka-Volterra system
    • 2557698 10.1016/j.jmaa.2009.07.053
    • Ton, T.V.: Survival of three species in a nonautonomous Lotka-Volterra system. J. Math. Anal. Appl. 362, 427-437 (2010)
    • (2010) J. Math. Anal. Appl. , vol.362 , pp. 427-437
    • Ton, T.V.1
  • 30
    • 0001733213 scopus 로고
    • Predation and resource partitioning in one predator-two prey model communities
    • 10.1086/283324
    • Vance, R.: Predation and resource partitioning in one predator-two prey model communities. Am. Nat. 112, 797-813 (1978)
    • (1978) Am. Nat. , vol.112 , pp. 797-813
    • Vance, R.1
  • 31
    • 47049084345 scopus 로고    scopus 로고
    • Asymptotic properties of hybrid diffusion systems
    • 2346378 10.1137/060649343
    • Zhu, C., Yin, G.: Asymptotic properties of hybrid diffusion systems. SIAM J. Control Optim. 46, 1155-1179 (2007)
    • (2007) SIAM J. Control Optim. , vol.46 , pp. 1155-1179
    • Zhu, C.1    Yin, G.2
  • 32
    • 72149109277 scopus 로고    scopus 로고
    • On hybrid competitive Lotka-Volterra ecosystems
    • 2671923 10.1016/j.na.2009.01.166
    • Zhu, C., Yin, G.: On hybrid competitive Lotka-Volterra ecosystems. Nonlinear Anal. 71, e1370-e1379 (2009)
    • (2009) Nonlinear Anal. , vol.71
    • Zhu, C.1    Yin, G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.