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Volumn 7, Issue 5, 2006, Pages 1205-1222

Some new results on the permanence and extinction of nonautonomous Gilpin-Ayala type competition model with delays

Author keywords

Delay; Extinction; Gilpin Ayala type competition system; Permanence

Indexed keywords

COMPUTATIONAL METHODS; COMPUTER SCIENCE; MATHEMATICAL MODELS; NONLINEAR CONTROL SYSTEMS; STABILITY CRITERIA; SYSTEM STABILITY;

EID: 33745167944     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2005.11.003     Document Type: Article
Times cited : (63)

References (36)
  • 1
    • 22844453576 scopus 로고    scopus 로고
    • Extinction of species in nonautonomous Lotka-Volterra systems
    • Ahmad S. Extinction of species in nonautonomous Lotka-Volterra systems. Proc. Am. Math. Soc. 127 (1999) 2905-2910
    • (1999) Proc. Am. Math. Soc. , vol.127 , pp. 2905-2910
    • Ahmad, S.1
  • 2
    • 0034172677 scopus 로고    scopus 로고
    • Average conditions for global asymptotic stability in a nonautonomous Lotka-Volterra system
    • Ahmad S., and Lazer A.C. Average conditions for global asymptotic stability in a nonautonomous Lotka-Volterra system. Nonlinear Anal. 40 (2000) 37-49
    • (2000) Nonlinear Anal. , vol.40 , pp. 37-49
    • Ahmad, S.1    Lazer, A.C.2
  • 3
    • 0015665417 scopus 로고
    • Competition between species: theoretical models and experimental tests
    • Ayala F.J., Gilpin M.E., and Eherenfeld J.G. Competition between species: theoretical models and experimental tests. Theoret. Popul. Biol. 4 (1973) 331-356
    • (1973) Theoret. Popul. Biol. , vol.4 , pp. 331-356
    • Ayala, F.J.1    Gilpin, M.E.2    Eherenfeld, J.G.3
  • 4
    • 4644236344 scopus 로고    scopus 로고
    • Global robust stability of interval cellular neural networks with time-varying delays
    • Chen A.P., Cao J.D., and Huang L.H. Global robust stability of interval cellular neural networks with time-varying delays. Chaos, Solitons & Fractals 23 3 (2005) 787-799
    • (2005) Chaos, Solitons & Fractals , vol.23 , Issue.3 , pp. 787-799
    • Chen, A.P.1    Cao, J.D.2    Huang, L.H.3
  • 5
    • 84978933417 scopus 로고    scopus 로고
    • Persistence and periodic orbits for two-species non-autonomous diffusion Lotka-Volterra models
    • Chen F.D. Persistence and periodic orbits for two-species non-autonomous diffusion Lotka-Volterra models. Appl. Math. J. Chin. Univ. Ser. B 19 4 (2004) 359-366
    • (2004) Appl. Math. J. Chin. Univ. Ser. B , vol.19 , Issue.4 , pp. 359-366
    • Chen, F.D.1
  • 6
    • 12244274373 scopus 로고    scopus 로고
    • Positive periodic solutions of neutral Lotka-Volterra system with feedback control
    • Chen F.D. Positive periodic solutions of neutral Lotka-Volterra system with feedback control. Appl. Math. Comput. 162 3 (2005) 1279-1302
    • (2005) Appl. Math. Comput. , vol.162 , Issue.3 , pp. 1279-1302
    • Chen, F.D.1
  • 7
    • 16244411081 scopus 로고    scopus 로고
    • Periodicity in a nonlinear predator-prey system with state dependent delays
    • (English Series)
    • Chen F.D. Periodicity in a nonlinear predator-prey system with state dependent delays. Acta Math. Appl. Sin. 21 1 (2005) 49-60 (English Series)
    • (2005) Acta Math. Appl. Sin. , vol.21 , Issue.1 , pp. 49-60
    • Chen, F.D.1
  • 8
    • 17644427702 scopus 로고    scopus 로고
    • On a nonlinear non-autonomous predator-prey model with diffusion and distributed delay
    • Chen F.D. On a nonlinear non-autonomous predator-prey model with diffusion and distributed delay. J. Comput. Appl. Math. 180 1 (2005) 33-49
    • (2005) J. Comput. Appl. Math. , vol.180 , Issue.1 , pp. 33-49
    • Chen, F.D.1
  • 9
    • 24944476496 scopus 로고    scopus 로고
    • F.D. Chen, The permanence and global attractivity of Lotka-Volterra competition system with feedback controls, Nonlinear Anal.: Real World Applications 7 (1) (2006) 133-143.
  • 10
    • 33745165510 scopus 로고    scopus 로고
    • F.D. Chen, Average conditions for permanence and extinction in nonautonomous Gilpin-Ayala competition model, Nonlinear Anal. RWA, in press.
  • 11
    • 33745168908 scopus 로고    scopus 로고
    • F.D. Chen, On a periodic multi-species ecological model, Appl. Math. Comput., in press.
  • 12
    • 4544258197 scopus 로고    scopus 로고
    • Sufficient conditions for the existence of positive periodic solutions of a class of neutral delay models with feedback control
    • Chen F.D., Lin F.X., and Chen X.X. Sufficient conditions for the existence of positive periodic solutions of a class of neutral delay models with feedback control. Appl. Math. Comput. 158 1 (2004) 45-68
    • (2004) Appl. Math. Comput. , vol.158 , Issue.1 , pp. 45-68
    • Chen, F.D.1    Lin, F.X.2    Chen, X.X.3
  • 13
    • 9744231393 scopus 로고    scopus 로고
    • Periodicity in a logistic type system with several delays
    • Chen F.D., and Lin S.J. Periodicity in a logistic type system with several delays. Comput. Math. Appl. 48 1-2 (2004) 35-44
    • (2004) Comput. Math. Appl. , vol.48 , Issue.1-2 , pp. 35-44
    • Chen, F.D.1    Lin, S.J.2
  • 14
    • 0346903415 scopus 로고    scopus 로고
    • Periodicity in a food-limited population model with toxicants and state dependent delays
    • Chen F.D., Sun D.X., and Lin F.X. Periodicity in a food-limited population model with toxicants and state dependent delays. J. Math. Anal. Appl. 288 1 (2003) 132-142
    • (2003) J. Math. Anal. Appl. , vol.288 , Issue.1 , pp. 132-142
    • Chen, F.D.1    Sun, D.X.2    Lin, F.X.3
  • 15
    • 2642556374 scopus 로고    scopus 로고
    • New results on positive periodic solutions of a periodic integro-differential competition system
    • Chen Y. New results on positive periodic solutions of a periodic integro-differential competition system. Appl. Math. Comput. 153 2 (2004) 557-565
    • (2004) Appl. Math. Comput. , vol.153 , Issue.2 , pp. 557-565
    • Chen, Y.1
  • 16
    • 0034324869 scopus 로고    scopus 로고
    • Global periodic solutions of a generalized n-species Gilpin-Ayala competition model
    • Fan M., and Wang K. Global periodic solutions of a generalized n-species Gilpin-Ayala competition model. Comput. Math. Appl. 40 (2000) 1141-1151
    • (2000) Comput. Math. Appl. , vol.40 , pp. 1141-1151
    • Fan, M.1    Wang, K.2
  • 17
    • 1942503803 scopus 로고    scopus 로고
    • Existence of positive periodic solution of an integral differential equation system
    • Fan M., and Wang K. Existence of positive periodic solution of an integral differential equation system. Acta Math. Sin. 44 3 (2001) 437-444
    • (2001) Acta Math. Sin. , vol.44 , Issue.3 , pp. 437-444
    • Fan, M.1    Wang, K.2
  • 18
    • 0032816634 scopus 로고    scopus 로고
    • Existence and global attractivity of positive periodic solutions of periodic n-species Lotka-Volterra competition systems with several deviating arguments
    • Fan M., Wang K., and Jiang D.Q. Existence and global attractivity of positive periodic solutions of periodic n-species Lotka-Volterra competition systems with several deviating arguments. Math. Biosci. 47 (1999) 47-61
    • (1999) Math. Biosci. , vol.47 , pp. 47-61
    • Fan, M.1    Wang, K.2    Jiang, D.Q.3
  • 19
    • 0015760853 scopus 로고
    • Global models of growth and competition
    • Gilpin M.E., and Ayala F.J. Global models of growth and competition. Proc. Nat. Acad. Sci. USA 70 (1973) 3590-3593
    • (1973) Proc. Nat. Acad. Sci. USA , vol.70 , pp. 3590-3593
    • Gilpin, M.E.1    Ayala, F.J.2
  • 20
    • 0017405632 scopus 로고
    • Stability in Gilpin and Ayala's model of competition
    • Goh B.S., and Agnew T.T. Stability in Gilpin and Ayala's model of competition. J. Math. Biol. 4 (1977) 275-279
    • (1977) J. Math. Biol. , vol.4 , pp. 275-279
    • Goh, B.S.1    Agnew, T.T.2
  • 22
    • 4344597711 scopus 로고    scopus 로고
    • Periodic solutions of a periodic Lotka-Volterra system with delay
    • Huo H.F., and Li W.T. Periodic solutions of a periodic Lotka-Volterra system with delay. Appl. Math. Comput. 156 3 (2004) 787-803
    • (2004) Appl. Math. Comput. , vol.156 , Issue.3 , pp. 787-803
    • Huo, H.F.1    Li, W.T.2
  • 23
    • 0031140839 scopus 로고    scopus 로고
    • Stability in Gilpin-Ayala competition models with diffusion
    • Liao X.X., and Li J. Stability in Gilpin-Ayala competition models with diffusion. Nonlinear Anal. Theoret. Methods Appl. 28 (1997) 1751-1758
    • (1997) Nonlinear Anal. Theoret. Methods Appl. , vol.28 , pp. 1751-1758
    • Liao, X.X.1    Li, J.2
  • 24
    • 0035285146 scopus 로고    scopus 로고
    • Periodic solutions of periodic delay Lotka-Volterra equations and systems
    • Li Y.K., and Kuang Y. Periodic solutions of periodic delay Lotka-Volterra equations and systems. J. Math. Anal. Appl. 255 1 (2001) 260-280
    • (2001) J. Math. Anal. Appl. , vol.255 , Issue.1 , pp. 260-280
    • Li, Y.K.1    Kuang, Y.2
  • 25
    • 0037054958 scopus 로고    scopus 로고
    • Permanence, extinction and balancing survival in nonautonomous Lotka-Volterra system with delays
    • Liu S.Q., and Chen L.S. Permanence, extinction and balancing survival in nonautonomous Lotka-Volterra system with delays. Appl. Math. Comput. 129 2-3 (2002) 481-499
    • (2002) Appl. Math. Comput. , vol.129 , Issue.2-3 , pp. 481-499
    • Liu, S.Q.1    Chen, L.S.2
  • 26
    • 21444434953 scopus 로고    scopus 로고
    • Extinction in nonautonomous competitive Loka-Volterra systems
    • Montes de Oca F., and Zeeman M.L. Extinction in nonautonomous competitive Loka-Volterra systems. Proc. Am. Math. Soc. 124 (1996) 3677-3687
    • (1996) Proc. Am. Math. Soc. , vol.124 , pp. 3677-3687
    • Montes de Oca, F.1    Zeeman, M.L.2
  • 27
    • 0039592797 scopus 로고    scopus 로고
    • On the nonautonomous Lotka-Volterra N-species competing systems
    • Teng Z. On the nonautonomous Lotka-Volterra N-species competing systems. Appl. Math. Comput. 114 (2000) 175-185
    • (2000) Appl. Math. Comput. , vol.114 , pp. 175-185
    • Teng, Z.1
  • 28
    • 0242396762 scopus 로고    scopus 로고
    • On the permanence and extinction in nonautonomous Lotka-Volterra competitive systems with delays
    • Teng Z.D. On the permanence and extinction in nonautonomous Lotka-Volterra competitive systems with delays. Acta Math. Sin. 44 2 (2001) 293-306
    • (2001) Acta Math. Sin. , vol.44 , Issue.2 , pp. 293-306
    • Teng, Z.D.1
  • 29
    • 0033115299 scopus 로고    scopus 로고
    • Uniform persistence and existence of strictly positive solutions in nonautonomous Lotka-Volterra competitive systems with delays
    • Teng Z.D., and Chen L.S. Uniform persistence and existence of strictly positive solutions in nonautonomous Lotka-Volterra competitive systems with delays. Comput. Math. Appl. 37 (1999) 61-71
    • (1999) Comput. Math. Appl. , vol.37 , pp. 61-71
    • Teng, Z.D.1    Chen, L.S.2
  • 30
    • 0034649920 scopus 로고    scopus 로고
    • Some new results of nonautonomous Lotka-Volterra competitive systems with delays
    • Teng Z.D., and Yu Y.H. Some new results of nonautonomous Lotka-Volterra competitive systems with delays. J. Math. Anal. Appl. 241 (2000) 254-275
    • (2000) J. Math. Anal. Appl. , vol.241 , pp. 254-275
    • Teng, Z.D.1    Yu, Y.H.2
  • 31
    • 58149363911 scopus 로고
    • An iterative scheme for the N-competing species problem
    • Tineo A. An iterative scheme for the N-competing species problem. J. Differential Equations 116 (1995) 1-15
    • (1995) J. Differential Equations , vol.116 , pp. 1-15
    • Tineo, A.1
  • 32
    • 0036151553 scopus 로고    scopus 로고
    • Periodic solution for a two-species nonautonomous competition Lotka-Volterra patch system with time delay
    • Zhang Z.Q., and Wang Z.C. Periodic solution for a two-species nonautonomous competition Lotka-Volterra patch system with time delay. J. Math. Anal. Appl. 265 1 (2002) 38-48
    • (2002) J. Math. Anal. Appl. , vol.265 , Issue.1 , pp. 38-48
    • Zhang, Z.Q.1    Wang, Z.C.2
  • 33
    • 0346279901 scopus 로고    scopus 로고
    • The qualitative analysis of N-species nonlinear prey-competition systems
    • Zhao J.D., and Chen W.C. The qualitative analysis of N-species nonlinear prey-competition systems. Appl. Math. Comput. 149 (2004) 567-576
    • (2004) Appl. Math. Comput. , vol.149 , pp. 567-576
    • Zhao, J.D.1    Chen, W.C.2
  • 34
    • 1842530716 scopus 로고    scopus 로고
    • Permanence in nonautonomous Loka-Volterra system with predator-prey
    • Zhao J.D., and Jiang J.F. Permanence in nonautonomous Loka-Volterra system with predator-prey. Appl. Math. Comput. 152 (2004) 99-109
    • (2004) Appl. Math. Comput. , vol.152 , pp. 99-109
    • Zhao, J.D.1    Jiang, J.F.2
  • 35
    • 7244224959 scopus 로고    scopus 로고
    • Average conditions for permanence and extinction in nonautonomous Lotka-Volterra system
    • Zhao J.D., and Jiang J.F. Average conditions for permanence and extinction in nonautonomous Lotka-Volterra system. J. Math. Anal. Appl. 299 (2004) 663-675
    • (2004) J. Math. Anal. Appl. , vol.299 , pp. 663-675
    • Zhao, J.D.1    Jiang, J.F.2
  • 36
    • 0142087731 scopus 로고    scopus 로고
    • The permanence and global attractivity in a nonautonomous Lotka-Volterra system
    • Zhao J.D., Jiang J.F., and Lazer A.C. The permanence and global attractivity in a nonautonomous Lotka-Volterra system. Nonlinear Anal.: Real World Applications 5 4 (2004) 265-276
    • (2004) Nonlinear Anal.: Real World Applications , vol.5 , Issue.4 , pp. 265-276
    • Zhao, J.D.1    Jiang, J.F.2    Lazer, A.C.3


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