메뉴 건너뛰기




Volumn 73, Issue 9, 2011, Pages 1969-2012

Survival Analysis of Stochastic Competitive Models in a Polluted Environment and Stochastic Competitive Exclusion Principle

Author keywords

Competitive model; Polluted environment; Stochastic competitive exclusion principle; Stochastic disturbance

Indexed keywords

ANIMAL; ARTICLE; BIOLOGICAL MODEL; COMPUTER SIMULATION; ECOSYSTEM; POLLUTION; SPECIES EXTINCTION; STATISTICS; SURVIVAL;

EID: 79961026130     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-010-9569-5     Document Type: Article
Times cited : (240)

References (53)
  • 3
    • 1942508139 scopus 로고    scopus 로고
    • Stochastic delay Lotka-Volterra model
    • Bahar, A., & Mao, X. (2004). Stochastic delay Lotka-Volterra model. J. Math. Anal. Appl., 292, 364-380.
    • (2004) J. Math. Anal. Appl. , vol.292 , pp. 364-380
    • Bahar, A.1    Mao, X.2
  • 4
    • 14844315022 scopus 로고    scopus 로고
    • Ratio-dependent predator-prey model: effect of environmental fluctuation and stability
    • Bandyopadhyay, M., & Chattopadhyay, J. (2005). Ratio-dependent predator-prey model: effect of environmental fluctuation and stability. Nonlinearity, 18, 913-936.
    • (2005) Nonlinearity , vol.18 , pp. 913-936
    • Bandyopadhyay, M.1    Chattopadhyay, J.2
  • 5
    • 0000735971 scopus 로고
    • Harvesting natural populations in a randomly fluctuating environment
    • Beddington, J. R., & May, R. M. (1977). Harvesting natural populations in a randomly fluctuating environment. Science, 197, 463-465.
    • (1977) Science , vol.197 , pp. 463-465
    • Beddington, J.R.1    May, R.M.2
  • 6
    • 0036241038 scopus 로고    scopus 로고
    • Variable effort harvesting models in random environments: generalization to density-dependent noise intensities
    • Braumann, C. A. (2002). Variable effort harvesting models in random environments: generalization to density-dependent noise intensities. Math. Biosci., 177& 178, 229-245.
    • (2002) Math. Biosci. , vol.177-178 , pp. 229-245
    • Braumann, C.A.1
  • 7
    • 33847329574 scopus 로고    scopus 로고
    • Itô versus Stratonovich calculus in random population growth
    • Braumann, C. A. (2007). Itô versus Stratonovich calculus in random population growth. Math. Biosci., 206, 81-107.
    • (2007) Math. Biosci. , vol.206 , pp. 81-107
    • Braumann, C.A.1
  • 8
    • 45049083412 scopus 로고    scopus 로고
    • Growth and extinction of populations in randomly varying environments
    • Braumann, C. A. (2008). Growth and extinction of populations in randomly varying environments. Comput. Math. Appl., 56, 631-644.
    • (2008) Comput. Math. Appl. , vol.56 , pp. 631-644
    • Braumann, C.A.1
  • 9
    • 77951878638 scopus 로고    scopus 로고
    • Competitive or weak cooperative stochastic Lotka-Volterra systems conditioned on non-extinction
    • doi:10.1007/s00285-009-0285-4
    • Cattiaux, P. Méléard, S. (2009). Competitive or weak cooperative stochastic Lotka-Volterra systems conditioned on non-extinction. J. Math. Biol., doi: 10. 1007/s00285-009-0285-4.
    • (2009) J. Math. Biol.
    • Cattiaux, P.1    Méléard, S.2
  • 10
    • 0030022552 scopus 로고    scopus 로고
    • Effect of toxic substances on a two species competitive system
    • Chattopadhyay, J. (1996). Effect of toxic substances on a two species competitive system. Ecol. Model., 84, 287-289.
    • (1996) Ecol. Model. , vol.84 , pp. 287-289
    • Chattopadhyay, J.1
  • 11
    • 33749063660 scopus 로고    scopus 로고
    • Dynamics of a stochastic Lotka-Volterra model perturbed by white noise
    • Du, N. H., & Sam, V. H. (2006). Dynamics of a stochastic Lotka-Volterra model perturbed by white noise. J. Math. Anal. Appl., 324, 82-97.
    • (2006) J. Math. Anal. Appl. , vol.324 , pp. 82-97
    • Du, N.H.1    Sam, V.H.2
  • 12
    • 0026276304 scopus 로고
    • Models for the effect of toxicant in single-species and predator-prey systems
    • Freedman, H. I., & Shukla, J. B. (1991). Models for the effect of toxicant in single-species and predator-prey systems. J. Math. Biol., 30, 15-30.
    • (1991) J. Math. Biol. , vol.30 , pp. 15-30
    • Freedman, H.I.1    Shukla, J.B.2
  • 13
    • 4344689629 scopus 로고
    • Persistence in stochastic food web models
    • Gard, T. C. (1984). Persistence in stochastic food web models. Bull. Math. Biol., 46, 357-370.
    • (1984) Bull. Math. Biol. , vol.46 , pp. 357-370
    • Gard, T.C.1
  • 14
    • 38249040858 scopus 로고
    • Stability for multispecies population models in random environments
    • Gard, T. C. (1986). Stability for multispecies population models in random environments. Nonlinear Anal., 10, 1411-1419.
    • (1986) Nonlinear Anal. , vol.10 , pp. 1411-1419
    • Gard, T.C.1
  • 16
    • 0026915354 scopus 로고
    • Stochastic models for toxicant-stressed populations
    • Gard, T. C. (1992). Stochastic models for toxicant-stressed populations. Bull. Math. Biol., 54, 827-837.
    • (1992) Bull. Math. Biol. , vol.54 , pp. 827-837
    • Gard, T.C.1
  • 17
    • 0034225547 scopus 로고    scopus 로고
    • The chemical Langevin equation
    • Gillespiea, D. T. (2000). The chemical Langevin equation. J. Chem. Phys., 113, 297-306.
    • (2000) J. Chem. Phys. , vol.113 , pp. 297-306
    • Gillespiea, D.T.1
  • 18
    • 0020571184 scopus 로고
    • Effects of toxicant on population: a qualitative approach I. Equilibrium environmental exposure
    • Hallam, T. G., Clark, C. E., & Lassider, R. R. (1983a). Effects of toxicant on population: a qualitative approach I. Equilibrium environmental exposure. Ecol. Model., 8, 291-304.
    • (1983) Ecol. Model. , vol.8 , pp. 291-304
    • Hallam, T.G.1    Clark, C.E.2    Lassider, R.R.3
  • 19
    • 0020959624 scopus 로고
    • Effects of toxicant on population: a qualitative approach II. First Order Kinetics
    • Hallam, T. G., Clark, C. E., & Jordan, G. S. (1983b). Effects of toxicant on population: a qualitative approach II. First Order Kinetics. J. Math. Biol., 18, 25-37.
    • (1983) J. Math. Biol. , vol.18 , pp. 25-37
    • Hallam, T.G.1    Clark, C.E.2    Jordan, G.S.3
  • 20
    • 0021217861 scopus 로고
    • Effects of toxicant on populations: a qualitative approach III. Environmental and food chain pathways
    • Hallam, T. G., & Deluna, J. L. (1984). Effects of toxicant on populations: a qualitative approach III. Environmental and food chain pathways. J. Theor. Biol., 109, 411-429.
    • (1984) J. Theor. Biol. , vol.109 , pp. 411-429
    • Hallam, T.G.1    Deluna, J.L.2
  • 21
    • 0022918323 scopus 로고
    • Persistence in population models with demographic fluctuations
    • Hallam, T. G., & Ma, Z. (1986). Persistence in population models with demographic fluctuations. J. Math. Biol., 24, 327-339.
    • (1986) J. Math. Biol. , vol.24 , pp. 327-339
    • Hallam, T.G.1    Ma, Z.2
  • 22
    • 0023063746 scopus 로고
    • On density and extinction in continuous population model
    • Hallam, T. G., & Ma, Z. (1987). On density and extinction in continuous population model. J. Math. Biol., 25, 191-201.
    • (1987) J. Math. Biol. , vol.25 , pp. 191-201
    • Hallam, T.G.1    Ma, Z.2
  • 23
    • 34248971890 scopus 로고
    • The competitive exclusion principle
    • Hardin, G. (1960). The competitive exclusion principle. Science, 131, 1292-1297.
    • (1960) Science , vol.131 , pp. 1292-1297
    • Hardin, G.1
  • 24
    • 34247200397 scopus 로고    scopus 로고
    • The survival analysis for a single-species population model in a polluted environment
    • He, J., & Wang, K. (2007). The survival analysis for a single-species population model in a polluted environment. Appl. Math. Model., 31, 2227-2238.
    • (2007) Appl. Math. Model. , vol.31 , pp. 2227-2238
    • He, J.1    Wang, K.2
  • 25
    • 60549095608 scopus 로고    scopus 로고
    • The survival analysis for a population in a polluted environment
    • He, J., & Wang, K. (2009). The survival analysis for a population in a polluted environment. Nonlinear Anal. Real World Appl., 10, 1555-1571.
    • (2009) Nonlinear Anal. Real World Appl. , vol.10 , pp. 1555-1571
    • He, J.1    Wang, K.2
  • 26
    • 0035439412 scopus 로고    scopus 로고
    • An algorithmic introduction to numerical simulation of stochastic differential equations
    • Higham, D. J. (2001). An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM Rev., 43, 525-546.
    • (2001) SIAM Rev. , vol.43 , pp. 525-546
    • Higham, D.J.1
  • 27
    • 0000816850 scopus 로고
    • Competition between plasmid-bearing and plasmid-free organisms in a chemostat with an inhibitorm
    • Hsu, S. B., Luo, T. K., & Waltman, P. (1995). Competition between plasmid-bearing and plasmid-free organisms in a chemostat with an inhibitorm. J. Math. Biol., 34, 225-238.
    • (1995) J. Math. Biol. , vol.34 , pp. 225-238
    • Hsu, S.B.1    Luo, T.K.2    Waltman, P.3
  • 28
    • 84972578664 scopus 로고
    • A comparison theorem for solutions of stochastic differential equations and its applications
    • Ikeda, N., & Watanabe, S. (1977). A comparison theorem for solutions of stochastic differential equations and its applications. Osaka J. Math. 619-633.
    • (1977) Osaka J. Math. , pp. 619-633
    • Ikeda, N.1    Watanabe, S.2
  • 29
    • 0020467741 scopus 로고
    • Application of a surplus production model to assess environmental impacts on exploited populations of Daphnia pluex in the laboratory
    • Jensen, A. L., & Marshall, J. S. (1982). Application of a surplus production model to assess environmental impacts on exploited populations of Daphnia pluex in the laboratory. Environ. Pollut., 28, 273-280.
    • (1982) Environ. Pollut. , vol.28 , pp. 273-280
    • Jensen, A.L.1    Marshall, J.S.2
  • 30
    • 67650711514 scopus 로고    scopus 로고
    • Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation
    • Li, X., & Mao, X. (2009). Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation. Discrete Contin. Dyn. Syst., 24, 523-545.
    • (2009) Discrete Contin. Dyn. Syst. , vol.24 , pp. 523-545
    • Li, X.1    Mao, X.2
  • 31
    • 0026265582 scopus 로고
    • The threshold of survival for system of two species in a polluted environment
    • Liu, H., & Ma, Z. (1991). The threshold of survival for system of two species in a polluted environment. J. Math. Biol., 30, 49-51.
    • (1991) J. Math. Biol. , vol.30 , pp. 49-51
    • Liu, H.1    Ma, Z.2
  • 32
    • 63549091562 scopus 로고    scopus 로고
    • Survival analysis of stochastic single-species population models in polluted environments
    • Liu, M., & Wang, K. (2009). Survival analysis of stochastic single-species population models in polluted environments. Ecol. Model., 220, 1347-1357.
    • (2009) Ecol. Model. , vol.220 , pp. 1347-1357
    • Liu, M.1    Wang, K.2
  • 33
    • 77952673264 scopus 로고    scopus 로고
    • Persistence and extinction of a stochastic single-specie model under regime switching in a polluted environment
    • Liu, M., & Wang, K. (2010). Persistence and extinction of a stochastic single-specie model under regime switching in a polluted environment. J. Theor. Biol., 264, 934-944.
    • (2010) J. Theor. Biol. , vol.264 , pp. 934-944
    • Liu, M.1    Wang, K.2
  • 34
    • 0016568164 scopus 로고
    • Persistence of dynamical systems under random perturbations
    • Ludwig, D. (1975). Persistence of dynamical systems under random perturbations. SIAM. Rev., 17, 605-640.
    • (1975) SIAM. Rev. , vol.17 , pp. 605-640
    • Ludwig, D.1
  • 35
    • 0023516230 scopus 로고
    • Effects of toxicants on population: a qualitative approach IV. Resources-consumer-toxicant models
    • Luna, J. T., & Hallam, T. G. (1987). Effects of toxicants on population: a qualitative approach IV. Resources-consumer-toxicant models. Ecol. Model., 35, 249-273.
    • (1987) Ecol. Model. , vol.35 , pp. 249-273
    • Luna, J.T.1    Hallam, T.G.2
  • 36
    • 34249314701 scopus 로고    scopus 로고
    • Stochastic population dynamics under regime switching
    • Luo, Q., & Mao, X. (2007). Stochastic population dynamics under regime switching. J. Math. Anal. Appl., 334, 69-84.
    • (2007) J. Math. Anal. Appl. , vol.334 , pp. 69-84
    • Luo, Q.1    Mao, X.2
  • 37
    • 0024488084 scopus 로고
    • The threshold of survival for systems in a fluctuating environment
    • Ma, Z., Song, B., & Hallam, T. G. (1989). The threshold of survival for systems in a fluctuating environment. Bull. Math. Biol., 51, 311-323.
    • (1989) Bull. Math. Biol. , vol.51 , pp. 311-323
    • Ma, Z.1    Song, B.2    Hallam, T.G.3
  • 38
    • 0242563961 scopus 로고    scopus 로고
    • Environmental Brownian noise suppresses explosions in populations dynamics
    • Mao, X., Marion, G., & Renshaw, E. (2002). Environmental Brownian noise suppresses explosions in populations dynamics. Stoch. Process. Appl., 97, 95-110.
    • (2002) Stoch. Process. Appl. , vol.97 , pp. 95-110
    • Mao, X.1    Marion, G.2    Renshaw, E.3
  • 39
    • 0242676984 scopus 로고    scopus 로고
    • Asymptotic behaviour of the stochastic Lotka-Volterra model
    • Mao, X., Sabanis, S., & Renshaw, E. (2003). Asymptotic behaviour of the stochastic Lotka-Volterra model. J. Math. Anal. Appl., 287, 141-156.
    • (2003) J. Math. Anal. Appl. , vol.287 , pp. 141-156
    • Mao, X.1    Sabanis, S.2    Renshaw, E.3
  • 40
    • 33746315382 scopus 로고    scopus 로고
    • Delay population dynamics and environmental noise
    • Mao, X. (2005). Delay population dynamics and environmental noise. Stoch. Dyn., 5, 149-162.
    • (2005) Stoch. Dyn. , vol.5 , pp. 149-162
    • Mao, X.1
  • 43
    • 27744447482 scopus 로고    scopus 로고
    • Predator-prey cycles from resonant amplification of demographic stochasticity
    • McKane, A. J., & Newman, T. J. (2005). Predator-prey cycles from resonant amplification of demographic stochasticity. Phys. Rev. Lett., 94, 218102.
    • (2005) Phys. Rev. Lett. , vol.94 , pp. 218102
    • McKane, A.J.1    Newman, T.J.2
  • 44
    • 77956757494 scopus 로고
    • The problem of oil pollution of the sea
    • London: Academic Press
    • Nelson, S. A. (1970). The problem of oil pollution of the sea. In Advances in marine biology (pp. 215-306). London: Academic Press.
    • (1970) Advances in Marine Biology , pp. 215-306
    • Nelson, S.A.1
  • 46
    • 53149141038 scopus 로고    scopus 로고
    • Asymptotic properties of stochastic population dynamics, Dynamics of Continuous
    • Pang, S., Deng, F., & Mao, X. (2008). Asymptotic properties of stochastic population dynamics, Dynamics of Continuous. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 15, 603-620.
    • (2008) Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. , vol.15 , pp. 603-620
    • Pang, S.1    Deng, F.2    Mao, X.3
  • 47
    • 33847295610 scopus 로고    scopus 로고
    • Influence of stochastic perturbation on prey-predator systems
    • Rudnicki, R., & Pichor, K. (2007). Influence of stochastic perturbation on prey-predator systems. Math. Biosci., 206, 108-119.
    • (2007) Math. Biosci. , vol.206 , pp. 108-119
    • Rudnicki, R.1    Pichor, K.2
  • 48
    • 4544242381 scopus 로고    scopus 로고
    • Dynamical model of a single-species system in a polluted environment
    • Samanta, G. P., & Maiti, A. (2004). Dynamical model of a single-species system in a polluted environment. J. Appl. Math. Comput., 16, 231-242.
    • (2004) J. Appl. Math. Comput. , vol.16 , pp. 231-242
    • Samanta, G.P.1    Maiti, A.2
  • 49
    • 0000342741 scopus 로고    scopus 로고
    • Simultaneous effect of two toxicants on biological species: a mathematical model
    • Shukla, J. B., & Dubey, B. (1996). Simultaneous effect of two toxicants on biological species: a mathematical model. J. Biol. Syst., 4, 109-130.
    • (1996) J. Biol. Syst. , vol.4 , pp. 109-130
    • Shukla, J.B.1    Dubey, B.2
  • 50
    • 0024484973 scopus 로고
    • Degradation and subsequent regeneration of a forestry resource: a mathematical model
    • Shukla, J. B., Freedman, H. I., Pal, V. N., Misra, O. P., Agarwal, M., & Shukla, A. (1989). Degradation and subsequent regeneration of a forestry resource: a mathematical model. Ecol. Model., 44, 219-229.
    • (1989) Ecol. Model. , vol.44 , pp. 219-229
    • Shukla, J.B.1    Freedman, H.I.2    Pal, V.N.3    Misra, O.P.4    Agarwal, M.5    Shukla, A.6
  • 51
    • 0029911718 scopus 로고    scopus 로고
    • A control problem in a polluted environment
    • Thomas, D. M., Snell, T. W., & Joffer, S. M. (1996). A control problem in a polluted environment. Math. Biosci., 133, 139-163.
    • (1996) Math. Biosci. , vol.133 , pp. 139-163
    • Thomas, D.M.1    Snell, T.W.2    Joffer, S.M.3
  • 52
    • 0017542932 scopus 로고
    • Random environments and stochastic calculus
    • Turelli, M. (1977). Random environments and stochastic calculus. Theor. Pop. Biol., 12, 140-178.
    • (1977) Theor. Pop. Biol. , vol.12 , pp. 140-178
    • Turelli, M.1
  • 53
    • 67349095282 scopus 로고    scopus 로고
    • On competitive Lotka-Volterra model in random environments
    • Zhu, C., & Yin, G. (2009). On competitive Lotka-Volterra model in random environments. J. Math. Anal. Appl., 357, 154-170.
    • (2009) J. Math. Anal. Appl. , vol.357 , pp. 154-170
    • Zhu, C.1    Yin, G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.