Abstract
Let f t be a flow on a compact metric space X and M be a closed invariant subset of X.
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References
N. P. Bhatia and G. P. Szegö: Stability Theory of Dynamical Systems. Grundlehren math. Wissensch. 161. Berlin - Heidelberg - New York: Springer. 1970.
R. Bowen: ω-limit sets for Axiom A diffeomorphisms. J. Diff. Equ. 18, 333–339 (1975).
G. Butler, H. I. Freedman and P. Waltman: Uniformly persistent systems. Proc. Amer. Math. Soc. 96, 425–430 (1986).
G. Butler, P. Waltman: Persistence in dynamical systems. J. Diff. Equ. 63, 255–263 (1986).
C. Conley: Isolated invariant sets and the Morse index. CBMS 38. Providence, R.I.: Amer. Math. Soc. 1978.
A. Fonda: Uniformly persistent semi-dynamical systems. Proc. Amer. Math. Soc. To appear.
H. I. Freedman and J. W.-H. So: Persistence in discrete semi-dynamical systems. Preprint (1987).
H. I. Freedman and P. Waltman: Mathematical analysis of some three-species food-chain models. Math. Biosci. 33, 257–276 (1977).
T. C. Gard and T. G. Hallam: Persistence of food webs: I. Lotka-Volterra food chains. Bull. Math. Biol. 41, 877–891 (1979).
B. M. Garay: Uniform persistence and chain recurrence. J. Math. Anal. Appl. To appear.
J. Hofbauer: A general cooperation theorem for hypercycles. Monatsh. Math. 91: 233–240 (1981).
J. Hofbauer: Heteroclinic cycles on the simplex. Proc. Int. Conf. Nonlinear Oscillations. Budapest 1987.
J. Hofbauer and K. Sigmund: Permanence for replicator equations. In: Dynamical Systems. Ed. A. B. Kurzhansky and K. Sigmund. Springer Lect. Notes Econ. Math. Systems 287. 1987.
J. Hofbauer and K. Sigmund: Dynamical Systems and the Theory of Evolution. Cambridge Univ. Press 1988.
V. Hutson: A theorem on average Ljapunov functions. Monatsh. Math. 98, 267–275 (1984).
W. Jansen: A permanence theorem for replicator and Lotka-Volterra systems. J. Math. Biol. 25, 411–422 (1987).
G. Kirlinger: Permanence of some four-species Lotka-Volterra systems. Dissertation. Universität Wien. 1987.
C. Robinson: Stability theorems and hyperbolicity in dynamical systems. Rocky Mountain J. Math. 7, 425–434 (1977).
P. Schuster, K. Sigmund and R. Wolff: Dynamical systems under constant organization. III. Cooperative and competitive behaviour of hypercycles. J. Diff. Equ. 32, 357–368 (1979).
T. Ura and I. Kimura: Sur le courant exterieur a une region invariante. Theoreme de Bendixson. Comm. Math. Univ. Sanctii Pauli 8, 23–39 (1960).
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© 1989 Kluwer Academic Publishers, Dordrecht, Holland
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Hofbauer, J. (1989). A Unified Approach to Persistence. In: Kurzhanski, A.B., Sigmund, K. (eds) Evolution and Control in Biological Systems. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2358-4_3
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DOI: https://doi.org/10.1007/978-94-009-2358-4_3
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