Permanence in ecological systems with spatial heterogeneity

Proceedings of the Royal Society of Edinburgh Section A: Mathematics - Tập 123 Số 3 - Trang 533-559 - 1993
Robert Stephen Cantrell1, Chris Cosners1, V. Hutson2
1Department of Mathematics and Computer Science, The University of Miami, Coral Gables, FL 33124, U.S.A.
2Department of Applied Mathematics, The University of Sheffield, Sheffield S102TN, U.K.

Tóm tắt

SynopsisA basic problem in population dynamics is that of finding criteria for the long-term coexistence of interacting species. An important aspect of the problem is determining how coexistence is affected by spatial dispersal and environmental heterogeneity. The object of this paper is to study the problem of coexistence for two interacting species dispersing through a spatially heterogeneous region. We model the population dynamics of the species with a system of two reaction–diffusion equations which we interpret as a semi-dynamical system. We say that the system is permanent if any state with all components positive initially must ultimately enter and remain within a fixed set of positive states that are strictly bounded away from zero in each component. Our analysis produces conditions that can be interpreted in a natural way in terms of environmental conditions and parameters, by combining the dynamic idea of permanence with the static idea of studying geometric problems via eigenvalue estimation.

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Tài liệu tham khảo

10.1007/978-1-4612-4838-5

10.1007/978-1-4684-0152-3

10.1007/BF00280826

Protter, 1967, Maximum Principles in Differential Equations

10.1016/0025-5564(89)90040-0

Levin, 1986, Mathematical Ecology

10.1216/RMJ-1987-17-2-301

10.1216/rmjm/1181073060

10.1007/BF01540776

10.1080/03605308008820162

10.1137/0520025

Friedman, 1969, Partial Differential Equations

10.1007/978-3-642-93111-6

10.1137/0137048

10.1016/0022-0396(85)90115-9

10.1090/S0002-9947-1984-0743741-4

Cosner, 1990, Reaction-Diffusion Equations

Cantrell, 1987, On the steady-state problem for the Volterra-Lotka competition model with diffusion, Houston J. Math., 13, 337

10.1017/S0308210500031802

Amann, 1985, Global existence for semilinear parabolic systems, J. Reine Angew. Math., 360, 47

10.1016/0025-5564(92)90078-B

10.1007/BFb0089647

Li, 1991, Positive solutions to general elliptic competition models, J. Differential and Integral Equations, 4, 817

10.1007/978-3-642-62006-5

Hofbauer, 1988, Dynamical Systems and the Theory of Evolution

10.1137/0138002

10.1016/0022-0396(86)90044-6

Cantrell, 1989, On the uniqueness and stability of positive solutions in the Lotka-Volterra competition model with diffusion, Houston J. Math., 15, 341

10.1016/0022-0396(79)90088-3

10.1137/0144080

Manes, 1973, Un'estensione della teoria variazionale classica degli antovalori per operatori ellittici del secondo ordine, Boll. Un. Mat. Ital., 7, 285

Okubo, 1980, Diffusion and Ecological Problems: Mathematical Models

10.1017/S030821050001876X

Mora, 1983, Semilinear parabolic problems define semiflows in Ck spaces, Trans. Amer. Math. Soc., 278, 21

Friedman, 1964, Partial Differential Equations of Parabolic Type

10.1090/S0002-9947-1988-0920151-1

10.1090/S0002-9939-1986-0822433-4

10.1016/0362-546X(87)90035-6

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Thông tin xuất bản

Proceedings of the Royal Society of Edinburgh Section A: Mathematics

Tập 123 Số 3

533-559

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