×

zbMATH — the first resource for mathematics

Persistence in dynamical systems. (English) Zbl 0603.58033
A continuous flow on a locally compact metric space with invariant boundary is considered. The criterion of the uniform persistence of the flow is obtained.
Reviewer: V.Sobolev

MSC:
37C10 Dynamics induced by flows and semiflows
92D25 Population dynamics (general)
Keywords:
persistence; flow
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bhatia, N.P; Szegő, G.P, Dynamical systems: stability theory and applications, () · Zbl 0993.37001
[2] Butler, G; Freedman, H; Waltman, P, Uniformly persistent systems, (), 425-430 · Zbl 0603.34043
[3] Freedman, H.I, Deterministic mathematical models in population ecology, (1980), Marcel Dekker New York · Zbl 0448.92023
[4] Freedman, H.I; Waltman, P, Persistence in models of three interacting predatorprey populations, Math. biosci., 68, 213-231, (1984) · Zbl 0534.92026
[5] Freedman, H.I; Waltman, P, Persistence in a model of three competitive populations, Math. biosci., 73, 89-101, (1985) · Zbl 0584.92018
[6] Gard, T.C; Hallam, T.G, Persistence in food webs. I. Lotka-Volterra food chains, Bull. math. biol., 41, 877-891, (1979) · Zbl 0422.92017
[7] Hale, J, Theory of functional differential equations, (1977), Springer-Verlag New York
[8] Hirsch, M.W; Pugh, C, Stable manifolds and hyperbolic sets, (), 133-165
[9] Hutson, V; Vickers, G.T, A criterion for permanent coexistence of species, with an application to a two-prey one-predator system, Math. biosci., 63, 253-269, (1983) · Zbl 0524.92023
[10] May, R.M; Leonard, W.J, Nonlinear aspects of competition between three species, SIAM J. appl. math., 29, 243-253, (1975) · Zbl 0314.92008
[11] Nitecki, Z, Differentiable dynamics, (1971), M.I.T. Press Cambridge
[12] Schuster, P; Sigmund, K; Wolff, R, On ω-limits for competition between three species, SIAM J. appl. math., 37, 49-54, (1979) · Zbl 0418.92016
[13] Sell, G; Sibuya, Y, Behaviour of solutions near a critical point, (), 501-506
[14] Smale, S, Differentiable dynamical systems, Bull. amer. math. soc., 73, 747-817, (1967) · Zbl 0202.55202
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.