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Volumn 127, Issue 4, 1999, Pages 993-1002

Successional stability of vector fields in dimension three

Author keywords

Ecological succession; Generic properties of vector fields; Population dynamics

Indexed keywords


EID: 22644449136     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9939-99-05169-2     Document Type: Article
Times cited : (7)

References (31)
  • 1
    • 0001188059 scopus 로고
    • Competitive exclusion
    • MR 82d:92029
    • R. A. Armstrong and R. McGehee, Competitive exclusion, Amer. Natur. 116 (1980), 151-170. MR 82d:92029
    • (1980) Amer. Natur. , vol.116 , pp. 151-170
    • Armstrong, R.A.1    McGehee, R.2
  • 2
    • 0011289134 scopus 로고
    • Heteroclinic networks on the tetrahedron
    • MR 95e:58128
    • W. Brannath, Heteroclinic networks on the tetrahedron, Nonlinearity 7 (1994), 1367-1384. MR 95e:58128
    • (1994) Nonlinearity , vol.7 , pp. 1367-1384
    • Brannath, W.1
  • 4
    • 0000036443 scopus 로고
    • Persistence in dynamical systems
    • MR 87k:54058
    • G. J. Butler and P. Waltman, Persistence in dynamical systems, J. Differential Equations 63 (1986), 255-263. MR 87k:54058
    • (1986) J. Differential Equations , vol.63 , pp. 255-263
    • Butler, G.J.1    Waltman, P.2
  • 5
    • 0026016966 scopus 로고
    • Invasion resistence, species build-up and community collapse in metapopulation models with interspecies competition
    • T. J. Case, Invasion resistence, species build-up and community collapse in metapopulation models with interspecies competition, Bio. J. of the Linn. Soc. 42 (1991), 239-266.
    • (1991) Bio. J. of the Linn. Soc. , vol.42 , pp. 239-266
    • Case, T.J.1
  • 6
    • 0003262604 scopus 로고
    • Isolated Invariant Sets and Morse Index
    • MR 80c:58009
    • C. Conley, Isolated Invariant Sets and Morse Index, Amer. Math. Soc., CBMS 38 (1978). MR 80c:58009
    • (1978) Amer. Math. Soc., CBMS , vol.38
    • Conley, C.1
  • 7
    • 0025201444 scopus 로고
    • The mechanics of community assembly and succession
    • J. A. Drake, The mechanics of community assembly and succession, J. Theor. Bio. 147 (1990), 213-233.
    • (1990) J. Theor. Bio. , vol.147 , pp. 213-233
    • Drake, J.A.1
  • 8
    • 38249023378 scopus 로고
    • Uniform persistence and chain recurrence, J. Math. Anal
    • MR 90h:54049
    • B. M. Garay, Uniform persistence and chain recurrence, J. Math. Anal, and Appl. 139 (1989), 372-382. MR 90h:54049
    • (1989) And Appl. , vol.139 , pp. 372-382
    • Garay, B.M.1
  • 9
    • 84951601313 scopus 로고
    • Chaos in three-species food chains
    • MR 95g:92019
    • A. Hastings and A. Klebanoff, Chaos in three-species food chains, J. Math. Biol. 32 (1994), 427-451. MR 95g:92019
    • (1994) J. Math. Biol. , vol.32 , pp. 427-451
    • Hastings, A.1    Klebanoff, A.2
  • 10
    • 0242589333 scopus 로고
    • Heteroclinic cycles in ecological differential equations
    • MR95i:34083
    • J. Hofbauer, Heteroclinic cycles in ecological differential equations, Tatra Mt. Math. Publ 4 (1994), 105-116. MR95i:34083
    • (1994) Tatra Mt. Math. Publ , vol.4 , pp. 105-116
    • Hofbauer, J.1
  • 12
    • 0000875842 scopus 로고
    • A mathematical theory for single-nutrient competition in continuous cultures of microorganisms
    • MR 55:7458
    • S. B. Hsu, S. P. Hubbell, and P. Waltman, A mathematical theory for single-nutrient competition in continuous cultures of microorganisms, SIAM J. Appl. Math. 32 (1977), 366-383. MR 55:7458
    • (1977) SIAM J. Appl. Math. , vol.32 , pp. 366-383
    • Hsu, S.B.1    Hubbell, S.P.2    Waltman, P.3
  • 13
    • 21444453892 scopus 로고    scopus 로고
    • Competitive exclusion and coexistence for competitive systems on ordered Danach spaces
    • MR 97d:92021
    • S. B. Hsu, H. L. Smith, and P. Waltman, Competitive exclusion and coexistence for competitive systems on ordered Danach spaces, Trans. Amer. Math. Soc. 348 (1996), 4083-4094. MR 97d:92021
    • (1996) Trans. Amer. Math. Soc. , vol.348 , pp. 4083-4094
    • Hsu, S.B.1    Smith, H.L.2    Waltman, P.3
  • 14
    • 0026616222 scopus 로고
    • Permanence and the dynamics of biological systems
    • MR 93d:92003
    • V. Hutson and K. Schmitt, Permanence and the dynamics of biological systems, Math. Biosci. 111(1992), 1-71. MR 93d:92003
    • (1992) Math. Biosci. , vol.111 , pp. 1-71
    • Hutson, V.1    Schmitt, K.2
  • 15
    • 0001225644 scopus 로고    scopus 로고
    • Robust heterodinic cycles
    • MR 98g:58126
    • M. Krupa, Robust heterodinic cycles, J. Nonlinear Sci. 7 (1997), 129-176. MR 98g:58126
    • (1997) J. Nonlinear Sci. , vol.7 , pp. 129-176
    • Krupa, M.1
  • 16
    • 84974489205 scopus 로고
    • Asymptotic stability of heterodinic cycles in systems with symmetry
    • MR 9Gg:58101
    • M. Krupa and I. Melbourne, Asymptotic stability of heterodinic cycles in systems with symmetry, Ergod. Th. fc Dynam. Sys. 15 (1995), 121-147. MR 9Gg:58101
    • (1995) Ergod. Th. fc Dynam. Sys. , vol.15 , pp. 121-147
    • Krupa, M.1    Melbourne, I.2
  • 17
    • 0000148939 scopus 로고
    • Contribution d la théorie des champs génériques
    • MR 29:2818a
    • I. Kupka, Contribution d la théorie des champs génériques, Contrib. Diff. Eqs. 2 (1963), 457-484. MR 29:2818a
    • (1963) Contrib. Diff. Eqs. , vol.2 , pp. 457-484
    • Kupka, I.1
  • 18
    • 0027446840 scopus 로고
    • Alternative permanent states of ecological communities
    • R. Law and R. D. Morton, Alternative permanent states of ecological communities, Ecology 74 (1993), 1347-1361.
    • (1993) Ecology , vol.74 , pp. 1347-1361
    • Law, R.1    Morton, R.D.2
  • 19
    • 0001159093 scopus 로고    scopus 로고
    • Permanence and the assembly of ecological communities
    • _, Permanence and the assembly of ecological communities, Ecology 77 (1996), 762775.
    • (1996) Ecology , vol.77 , pp. 762775
  • 21
    • 0001206282 scopus 로고
    • Filtrations, decompositions and explosions
    • MR 52:15561
    • Z. Nitecki and M. Shub, Filtrations, decompositions and explosions, Amer. J. Math. 97 (1975), 1029-1047. MR 52:15561
    • (1975) Amer. J. Math. , vol.97 , pp. 1029-1047
    • Nitecki, Z.1    Shub, M.2
  • 23
    • 1542466748 scopus 로고
    • On an approximation theorem of Kupka and Smale
    • MR 35:499
    • M. M. Peixoto, On an approximation theorem of Kupka and Smale, J. Differential Equations 3 (1966), 214-227. MR 35:499
    • (1966) J. Differential Equations , vol.3 , pp. 214-227
    • Peixoto, M.M.1
  • 24
    • 0020764629 scopus 로고
    • Community assembly and food web stability
    • W. M. Post and S. L. Pimm, Community assembly and food web stability, Math. Biosci. 64 (1983), 169-192.
    • (1983) Math. Biosci. , vol.64 , pp. 169-192
    • Post, W.M.1    Pimm, S.L.2
  • 25
    • 0001551716 scopus 로고
    • An improved closing lemma and a general density theorem
    • MR 37:2257
    • C. Pugh, An improved closing lemma and a general density theorem, Amer. J. Math 89 (1967), 1010-1021. MR 37:2257
    • (1967) Amer. J. Math , vol.89 , pp. 1010-1021
    • Pugh, C.1
  • 26
    • 0003135857 scopus 로고    scopus 로고
    • Generalist and specialist predators that mediate permanence in ecological communities
    • MR 98k:92017
    • S. J. Schreiber, Generalist and specialist predators that mediate permanence in ecological communities, J. Math. Bio. 36 (1997), 133-148. MR 98k:92017
    • (1997) J. Math. Bio. , vol.36 , pp. 133-148
    • Schreiber, S.J.1
  • 27
    • 0000491205 scopus 로고
    • Dynamical systems under constant organization 3: Cooperative and competitive behavior of hypercycles
    • MR 82b:34035b
    • P. Schuster, K. Sigmund, and R. Wolff, Dynamical systems under constant organization 3: Cooperative and competitive behavior of hypercycles, J. Differential Equations 32 (1979), 357-368. MR 82b:34035b
    • (1979) J. Differential Equations , vol.32 , pp. 357-368
    • Schuster, P.1    Sigmund, K.2    Wolff, R.3
  • 28
    • 0003389030 scopus 로고
    • Stable manifolds for differential equations and diffeomorphisms
    • MR 29:2818b
    • S. Smale, Stable manifolds for differential equations and diffeomorphisms, Ann. Scuola Normale Superiore Pisa 18 (1963), 97-116. MR 29:2818b
    • (1963) Ann. Scuola Normale Superiore Pisa , vol.18 , pp. 97-116
    • Smale, S.1
  • 29
    • 0028483826 scopus 로고
    • Competition for a single limiting resource in continuous culture: The variable-yield model
    • MR 95b:92014
    • H. L. Smith and P. Waltman, Competition for a single limiting resource in continuous culture: the variable-yield model, SIAM J. Appl. Math. 54 (1994), 1113-1131. MR 95b:92014
    • (1994) SIAM J. Appl. Math. , vol.54 , pp. 1113-1131
    • Smith, H.L.1    Waltman, P.2
  • 30
    • 84968514083 scopus 로고
    • Smoothing derivatives of functions and applications
    • MR 40:4974
    • F. W. Wilson, Smoothing derivatives of functions and applications, Trans. Amer. Math. Soc. 139 (1969), 413-428. MR 40:4974
    • (1969) Trans. Amer. Math. Soc. , vol.139 , pp. 413-428
    • Wilson, F.W.1
  • 31
    • 0024639568 scopus 로고
    • Successful invasion of a food web in a chemostat
    • MR 90f:92027
    • G. S. K. Wolkowicz, Successful invasion of a food web in a chemostat, Math. Biosci. 93 (1989), 249-268. MR 90f:92027
    • (1989) Math. Biosci. , vol.93 , pp. 249-268
    • Wolkowicz, G.S.K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.