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Dynamics of competitive systems with a single common limiting factor
1. | Faculty of Engineering, University of Miyazaki, Gakuen Kibanadai Nishi 1-1, Miyazaki 889-2192, Japan |
References:
[1] |
R. A. Armstrong and R. McGehee, Coexistence of species competing for shared resources, Theoretical Population Biology, 9 (1976), 317-328.
doi: 10.1016/0040-5809(76)90051-4. |
[2] |
R. A. Armstrong and R. McGehee, Coexistence of two competitors on one resource, Journal of Theoretical Biology, 56 (1976), 499-502.
doi: 10.1016/S0022-5193(76)80089-6. |
[3] |
R. A. Armstrong and R. McGehee, Competitive exclusion, The American Naturalist, 115 (1980), 151-170.
doi: 10.1086/283553. |
[4] |
M. Hirsch and H. Smith, Monotone dynamical systems, In A. Canada, P. Drabek, and A. Fonda, editors, Ordinary Differential Equations, Elsevier, II (2005), 239-357. |
[5] |
J. Hofbauer, An index theorem for dissipative semiflows, Rocky Mountain J. Math., 20 (1990), 1017-1031. Geoffrey J. Butler Memorial Conference in Differential Equations and Mathematical Biology (Edmonton, AB, 1988).
doi: 10.1216/rmjm/1181073059. |
[6] |
J. Hofbauer and K. Sigmund, The Theory of Evolution and Dynamical Systems: Mathematical Aspects of Selection, Cambridge University Press Cambridge, 1988. |
[7] |
J. Hofbauer and K. Sigmund, Evolutionary Games and Population Dynamics, Cambridge University Press, Cambridge, 1998.
doi: 10.1017/CBO9781139173179. |
[8] |
R. D. Holt, J. Grover and D. Tilman, Simple rules for interspecific dominance in systems with exploitative and apparent competition, American Naturalist, 144 (1994), 741-771.
doi: 10.1086/285705. |
[9] |
S. A. Levin, Community equilibria and stability, and an extension of the competitive exclusion principle, The American Naturalist, 104 (1970), 413-423.
doi: 10.1086/282676. |
[10] |
D. Logofet, Matrices and Graphs: Stability Problems in Mathematical Ecology, CRC Press, Boca Raton, Florida, 1993. |
[11] |
R. McGehee and R. A. Armstrong, Some mathematical problems concerning the ecological principle of competitive exclusion, Journal of Differential Equations, 23 (1977), 30-52.
doi: 10.1016/0022-0396(77)90135-8. |
[12] |
J. Moré and W. Rheinboldt, On P- and S-functions and related classes of n-dimensional nonlinear mappings, Linear Algebra and its Applications, 6 (1973), 45-68.
doi: 10.1016/0024-3795(73)90006-2. |
[13] |
J. J. Moré, Classes of functions and feasibility conditions in nonlinear complementarity problems, Mathematical Programming, 6 (1974), 327-338.
doi: 10.1007/BF01580248. |
[14] |
F. Scudo and J. Ziegler, Lecture Notes in Biomathematic, volume 22 of Lecture notes in Biomathematics, Sprinter, 1978. |
[15] |
N. Shigesada, K. Kawasaki and E. Teramoto, The effects of interference competition on stability, structure and invasion of a multispecies system, J. Math. Biol., 21 (1984), 97-113.
doi: 10.1007/BF00277664. |
[16] |
H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, Mathematical Surveys and Monographs. American Mathematical Society, 1995. |
[17] |
Y. Takeuchi and N. Adachi, The existence of globally stable equilibria of ecosystems of the generalized Volterra type, J. Math. Biol., 10 (1980), 401-415.
doi: 10.1007/BF00276098. |
[18] |
Y. Takeuchi and N. Adachi, Existence of stable equilibrium point for dynamical systems of Volterra type, J. Math. Anal. Appl., 79 (1981), 141-162.
doi: 10.1016/0022-247X(81)90015-9. |
[19] |
Y. Takeuchi, N. Adachi and H. Tokumaru, Global stability of ecosystems of the generalized Volterra type, Math. Biosci., 42 (1978), 119-136.
doi: 10.1016/0025-5564(78)90010-X. |
[20] |
Y. Takeuchi, N. Adachi and H. Tokumaru, The stability of generalized Volterra equations, J. Math. Anal. Appl., 62 (1978), 453-473.
doi: 10.1016/0022-247X(78)90139-7. |
show all references
References:
[1] |
R. A. Armstrong and R. McGehee, Coexistence of species competing for shared resources, Theoretical Population Biology, 9 (1976), 317-328.
doi: 10.1016/0040-5809(76)90051-4. |
[2] |
R. A. Armstrong and R. McGehee, Coexistence of two competitors on one resource, Journal of Theoretical Biology, 56 (1976), 499-502.
doi: 10.1016/S0022-5193(76)80089-6. |
[3] |
R. A. Armstrong and R. McGehee, Competitive exclusion, The American Naturalist, 115 (1980), 151-170.
doi: 10.1086/283553. |
[4] |
M. Hirsch and H. Smith, Monotone dynamical systems, In A. Canada, P. Drabek, and A. Fonda, editors, Ordinary Differential Equations, Elsevier, II (2005), 239-357. |
[5] |
J. Hofbauer, An index theorem for dissipative semiflows, Rocky Mountain J. Math., 20 (1990), 1017-1031. Geoffrey J. Butler Memorial Conference in Differential Equations and Mathematical Biology (Edmonton, AB, 1988).
doi: 10.1216/rmjm/1181073059. |
[6] |
J. Hofbauer and K. Sigmund, The Theory of Evolution and Dynamical Systems: Mathematical Aspects of Selection, Cambridge University Press Cambridge, 1988. |
[7] |
J. Hofbauer and K. Sigmund, Evolutionary Games and Population Dynamics, Cambridge University Press, Cambridge, 1998.
doi: 10.1017/CBO9781139173179. |
[8] |
R. D. Holt, J. Grover and D. Tilman, Simple rules for interspecific dominance in systems with exploitative and apparent competition, American Naturalist, 144 (1994), 741-771.
doi: 10.1086/285705. |
[9] |
S. A. Levin, Community equilibria and stability, and an extension of the competitive exclusion principle, The American Naturalist, 104 (1970), 413-423.
doi: 10.1086/282676. |
[10] |
D. Logofet, Matrices and Graphs: Stability Problems in Mathematical Ecology, CRC Press, Boca Raton, Florida, 1993. |
[11] |
R. McGehee and R. A. Armstrong, Some mathematical problems concerning the ecological principle of competitive exclusion, Journal of Differential Equations, 23 (1977), 30-52.
doi: 10.1016/0022-0396(77)90135-8. |
[12] |
J. Moré and W. Rheinboldt, On P- and S-functions and related classes of n-dimensional nonlinear mappings, Linear Algebra and its Applications, 6 (1973), 45-68.
doi: 10.1016/0024-3795(73)90006-2. |
[13] |
J. J. Moré, Classes of functions and feasibility conditions in nonlinear complementarity problems, Mathematical Programming, 6 (1974), 327-338.
doi: 10.1007/BF01580248. |
[14] |
F. Scudo and J. Ziegler, Lecture Notes in Biomathematic, volume 22 of Lecture notes in Biomathematics, Sprinter, 1978. |
[15] |
N. Shigesada, K. Kawasaki and E. Teramoto, The effects of interference competition on stability, structure and invasion of a multispecies system, J. Math. Biol., 21 (1984), 97-113.
doi: 10.1007/BF00277664. |
[16] |
H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, Mathematical Surveys and Monographs. American Mathematical Society, 1995. |
[17] |
Y. Takeuchi and N. Adachi, The existence of globally stable equilibria of ecosystems of the generalized Volterra type, J. Math. Biol., 10 (1980), 401-415.
doi: 10.1007/BF00276098. |
[18] |
Y. Takeuchi and N. Adachi, Existence of stable equilibrium point for dynamical systems of Volterra type, J. Math. Anal. Appl., 79 (1981), 141-162.
doi: 10.1016/0022-247X(81)90015-9. |
[19] |
Y. Takeuchi, N. Adachi and H. Tokumaru, Global stability of ecosystems of the generalized Volterra type, Math. Biosci., 42 (1978), 119-136.
doi: 10.1016/0025-5564(78)90010-X. |
[20] |
Y. Takeuchi, N. Adachi and H. Tokumaru, The stability of generalized Volterra equations, J. Math. Anal. Appl., 62 (1978), 453-473.
doi: 10.1016/0022-247X(78)90139-7. |
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