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Volumn 53, Issue 3, 2006, Pages 365-384

Globally attracting fixed points in higher order discrete population models

Author keywords

Age structured model; Clark model; Delayed population model; Global attractor; Global stability; Permanence

Indexed keywords

ANIMAL; ARTICLE; BIOLOGICAL MODEL; MATHEMATICS; POPULATION DYNAMICS; WHALE;

EID: 33748203296     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-006-0014-1     Document Type: Article
Times cited : (25)

References (37)
  • 2
    • 0002562983 scopus 로고
    • Dynamics in one dimension
    • Springer, Berlin Heidelberg New York
    • Block, L.S., Coppel, W.A.: Dynamics in one dimension. Lecture notes in Mathematics, vol. 1513. Springer, Berlin Heidelberg New York (1992)
    • (1992) Lecture Notes in Mathematics , vol.1513
    • Block, L.S.1    Coppel, W.A.2
  • 3
    • 0000978282 scopus 로고
    • Further analysis of Clark's delayed recruitment model
    • Botsford, L.W.: Further analysis of Clark's delayed recruitment model. Bull. Math. Biol. 54, 275-293 (1992)
    • (1992) Bull. Math. Biol. , vol.54 , pp. 275-293
    • Botsford, L.W.1
  • 4
    • 33746927181 scopus 로고    scopus 로고
    • On linear perturbations of the Ricker model
    • DOI: 10.1016/j.mbs.2006.04.008
    • Braverman, E., Kinzebulatov, D.: On linear perturbations of the Ricker model. Math. Biosci. DOI: 10.1016/j.mbs.2006.04.008 (2006)
    • (2006) Math. Biosci.
    • Braverman, E.1    Kinzebulatov, D.2
  • 5
    • 0017194516 scopus 로고
    • A delayed recruitment model of population dynamics with an application to baleen whale populations
    • Clark, C.W.: A delayed recruitment model of population dynamics with an application to baleen whale populations. J. Math. Biol. 3, 381-391 (1976)
    • (1976) J. Math. Biol. , vol.3 , pp. 381-391
    • Clark, C.W.1
  • 6
    • 0023932252 scopus 로고
    • Stability of discrete one-dimensional population models
    • Cull, P.: Stability of discrete one-dimensional population models. Bull. Math. Biol. 50, 67-75 (1988)
    • (1988) Bull. Math. Biol. , vol.50 , pp. 67-75
    • Cull, P.1
  • 7
    • 33646014602 scopus 로고    scopus 로고
    • Stability in one-dimensional models
    • Cull, P.: Stability in one-dimensional models. Sci. Math. Jpn. 8, 349-357 (2003)
    • (2003) Sci. Math. Jpn. , vol.8 , pp. 349-357
    • Cull, P.1
  • 8
    • 0037299394 scopus 로고    scopus 로고
    • The global attractivity of difference equations of nonincreasing nonlinearities with applications
    • El-Morshedy, H.A.: The global attractivity of difference equations of nonincreasing nonlinearities with applications. Comput. Math. Appl. 45, 749-758 (2003)
    • (2003) Comput. Math. Appl. , vol.45 , pp. 749-758
    • El-Morshedy, H.A.1
  • 9
    • 12344327784 scopus 로고    scopus 로고
    • Convergence to equilibria in discrete population models
    • El-Morshedy, H.A., Liz, E.: Convergence to equilibria in discrete population models. J. Differ. Equ. Appl. 11, 117-131 (2005)
    • (2005) J. Differ. Equ. Appl. , vol.11 , pp. 117-131
    • El-Morshedy, H.A.1    Liz, E.2
  • 10
    • 0010935173 scopus 로고
    • Stability of a class of delay-difference equations
    • Fisher, M.E.: Stability of a class of delay-difference equations. Nonlinear Anal. 8, 645-654 (1984)
    • (1984) Nonlinear Anal. , vol.8 , pp. 645-654
    • Fisher, M.E.1
  • 11
    • 0021329114 scopus 로고
    • Stability results for delayed-recruitment models in population dynamics
    • Fisher, M.E., Goh, B.S.: Stability results for delayed-recruitment models in population dynamics. J. Math. Biol. 19, 147-156 (1984)
    • (1984) J. Math. Biol. , vol.19 , pp. 147-156
    • Fisher, M.E.1    Goh, B.S.2
  • 12
    • 0018595206 scopus 로고
    • Some stability conditions for discrete-time single species models
    • Fisher, M.E., Goh, B.S., Vincent, T.L.: Some stability conditions for discrete-time single species models. Bull. Math. Biol. 41, 861-875 (1979)
    • (1979) Bull. Math. Biol. , vol.41 , pp. 861-875
    • Fisher, M.E.1    Goh, B.S.2    Vincent, T.L.3
  • 14
    • 23044533954 scopus 로고    scopus 로고
    • Global attractivity and persistence in a discrete population model
    • Gyori, I., Trofimchuk, S.: Global attractivity and persistence in a discrete population model. J. Differ. Equ. Appl. 6, 647-665 (2000)
    • (2000) J. Differ. Equ. Appl. , vol.6 , pp. 647-665
    • Gyori, I.1    Trofimchuk, S.2
  • 15
    • 4944240015 scopus 로고    scopus 로고
    • Sharkovsky orderings of higher order difference equations
    • an der Heiden, U., Liang, M.-L.: Sharkovsky orderings of higher order difference equations. Discrete Contin. Dyn. Syst. 11, 599-614 (2004)
    • (2004) Discrete Contin. Dyn. Syst. , vol.11 , pp. 599-614
    • An Der Heiden, U.1    Liang, M.-L.2
  • 16
    • 0020362118 scopus 로고
    • The dynamics of production and destruction: Analytic insight into complex behavior
    • an der Heiden, U., Mackey, M.C.: The dynamics of production and destruction: analytic insight into complex behavior. J. Math. Biol. 16, 75-101 (1982)
    • (1982) J. Math. Biol. , vol.16 , pp. 75-101
    • An Der Heiden, U.1    Mackey, M.C.2
  • 17
    • 0000232059 scopus 로고
    • On global stability in a nonlinear discrete model
    • Ivanov, A.F.: On global stability in a nonlinear discrete model. Nonlinear Anal. 23, 1383-1389 (1994)
    • (1994) Nonlinear Anal. , vol.23 , pp. 1383-1389
    • Ivanov, A.F.1
  • 18
    • 0001046750 scopus 로고
    • The dynamics of some discrete population models
    • Karakostas, G., Philos, Ch.G., Sficas, Y.G.: The dynamics of some discrete population models. Nonlinear Anal. 17, 1069-1084 (1991)
    • (1991) Nonlinear Anal. , vol.17 , pp. 1069-1084
    • Karakostas, G.1    Philos, Ch.G.2    Sficas, Y.G.3
  • 19
    • 3042510840 scopus 로고
    • Global Behavior of Nonlinear Difference Equations of Higher Order with Applications
    • Kluwer, Dordrecht
    • Kocić, V.L., Ladas, G.: Global Behavior of Nonlinear Difference Equations of Higher Order with Applications. Mathematics and its Applications, vol. 256. Kluwer, Dordrecht (1993)
    • (1993) Mathematics and Its Applications , vol.256
    • Kocić, V.L.1    Ladas, G.2
  • 21
    • 0016946745 scopus 로고
    • A note on difference delay equations
    • Levin, S.A., May, R.M.: A note on difference delay equations. Theor. Pop. Biol. 9, 178-187 (1976)
    • (1976) Theor. Pop. Biol. , vol.9 , pp. 178-187
    • Levin, S.A.1    May, R.M.2
  • 22
    • 2442502476 scopus 로고    scopus 로고
    • A global stability criterion for scalar functional differential equations
    • Liz, E., Tkachenko, V., Trofimchuk, S.: A global stability criterion for scalar functional differential equations. SIAM J. Math. Anal. 35, 596-622 (2003)
    • (2003) SIAM J. Math. Anal. , vol.35 , pp. 596-622
    • Liz, E.1    Tkachenko, V.2    Trofimchuk, S.3
  • 23
    • 30144432115 scopus 로고    scopus 로고
    • Global stability in discrete population models with delayed-density dependence
    • Liz, E., Tkachenko, V., Trofimchuk, S.: Global stability in discrete population models with delayed-density dependence. Math. Biosci. 199, 26-37 (2006)
    • (2006) Math. Biosci. , vol.199 , pp. 26-37
    • Liz, E.1    Tkachenko, V.2    Trofimchuk, S.3
  • 24
    • 0017714604 scopus 로고
    • Oscillation and chaos in physiological control systems
    • Mackey, M.C., Glass, L.: Oscillation and chaos in physiological control systems. Science 197, 287-289 (1977)
    • (1977) Science , vol.197 , pp. 287-289
    • Mackey, M.C.1    Glass, L.2
  • 25
    • 0016394337 scopus 로고
    • Biological populations with nonoverlapping generations: Stable points, stable cycles, and chaos
    • May, R.M.: Biological populations with nonoverlapping generations: stable points, stable cycles, and chaos. Science 186, 645-647 (1974)
    • (1974) Science , vol.186 , pp. 645-647
    • May, R.M.1
  • 26
    • 0017185443 scopus 로고
    • Simple mathematical models with very complicated dynamics
    • May, R.M.: Simple mathematical models with very complicated dynamics. Nature 261, 459-467 (1976)
    • (1976) Nature , vol.261 , pp. 459-467
    • May, R.M.1
  • 27
  • 28
    • 33748204914 scopus 로고
    • An augmented Clark model for stability of populations
    • Mertz, G., Myers, R.A.: An augmented Clark model for stability of populations. Math. Biosci. 64, 227-231 (1983)
    • (1983) Math. Biosci. , vol.64 , pp. 227-231
    • Mertz, G.1    Myers, R.A.2
  • 29
    • 38949177846 scopus 로고
    • Chaos, noise, and extincion in models of population growth
    • Milton, J.G., Bélair, J.: Chaos, noise, and extincion in models of population growth. Theor. Popul. Biol. 37, 273-290 (1990)
    • (1990) Theor. Popul. Biol. , vol.37 , pp. 273-290
    • Milton, J.G.1    Bélair, J.2
  • 30
    • 0003475470 scopus 로고
    • Springer, Berlin Heidelberg New York
    • Murray, J.D.: Mathematical Biology. Springer, Berlin Heidelberg New York (1993)
    • (1993) Mathematical Biology
    • Murray, J.D.1
  • 32
    • 0038229629 scopus 로고
    • On global stability of discrete population models
    • Rosenkranz, G.: On global stability of discrete population models. Math. Biosci. 64, 227-231 (1983)
    • (1983) Math. Biosci. , vol.64 , pp. 227-231
    • Rosenkranz, G.1
  • 33
    • 0031488255 scopus 로고    scopus 로고
    • The impossibility of unstable, globally attracting fixed points for continuous mapping of the line
    • Sedaghat, H.: The impossibility of unstable, globally attracting fixed points for continuous mapping of the line. Am. Math. Monthly 104, 356-358 (1997)
    • (1997) Am. Math. Monthly , vol.104 , pp. 356-358
    • Sedaghat, H.1
  • 35
    • 0001273984 scopus 로고
    • Stable orbits and bifurcation of maps of the interval
    • Singer, D.: Stable orbits and bifurcation of maps of the interval. SIAM J. Appl. Math. 35, 260-267 (1978)
    • (1978) SIAM J. Appl. Math. , vol.35 , pp. 260-267
    • Singer, D.1
  • 37
    • 12744261096 scopus 로고    scopus 로고
    • Global stability in difference equations satisfying the generalized Yorke condition
    • Tkachenko, V., Trofimchuk, S.: Global stability in difference equations satisfying the generalized Yorke condition. J. Math. Anal. Appl. 303, 173-187 (2005)
    • (2005) J. Math. Anal. Appl. , vol.303 , pp. 173-187
    • Tkachenko, V.1    Trofimchuk, S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.