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Bardi, Martino

Predator-prey models in periodically fluctuating environments. (English) Zbl 0466.92019

J. Math. Biol. 12, 127-140 (1981).
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Cited in 24 Documents

MSC:

92D25 Population dynamics (general)
45J05 Integro-ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
92D40 Ecology

Keywords:

predator-prey models; periodically fluctuating environments; nonautonomous periodic systems; nonlinear eigenvalue problems; bifurcation theory
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References:

[1] Coppel, W. A.: Stability and asymptotic behaviour of differential equations. Boston: Heath 1965 · Zbl 0154.09301
[2] Crandall, M. G., Rabinowitz, P. H.: Bifurcation from simple eigenvalues. J. Functional Analysis 8, 321-340 (1971) · Zbl 0219.46015 · doi:10.1016/0022-1236(71)90015-2
[3] Cushing, J. M.: Periodic time-dependent predator-prey systems. SIAM J. Appl. Math. 32, 82-95 (1977) · Zbl 0348.34031 · doi:10.1137/0132006
[4] Cushing, J. M: Integrodifferential equations and delay models in populations dynamics. Lecture Notes in Biomath. 20, Springer-Verlag (1977) · Zbl 0363.92014
[5] Cushing, J. M.: Stable positive periodic solutions of the time-dependent logistic equation under possible hereditary influences. J. Math. Anal. Appl. 60, 747-754 (1977) · Zbl 0367.34032 · doi:10.1016/0022-247X(77)90014-2
[6] Dancer, E. N.: On the structure of solutions of nonlinear eigenvalue problems. Indiana Univ. Math. J. 23, 1069-1076 (1974) · Zbl 0276.47051 · doi:10.1512/iumj.1974.23.23087
[7] Halanay, A.: Differential equations: Stability, oscillations, time lags. New York: Academic Press 1966 · Zbl 0144.08701
[8] Holling, C. S.: The functional response of predators to prey density and its role in mimicry and population regulation. Mem. Entomol. Soc. Can. 45, 1-60 (1965)
[9] Ize, J.: Bifurcation theory for Fredholm operators. Mem. Amer. Math. Soc. 174 (1976) · Zbl 0338.47032
[10] Johnson, F. H., Eyring, H., Polissar, M. J.: The kinetic basis of molecular biology. New York: Wiley 1954
[11] Krasnosel’skii, M. A.: Topological methods in the theory of nonlinear integral equations. Oxford: Pergamon Press 1964
[12] Leslie, P. H.: Some further notes on the use of matrices in populations mathematics. Biometrika 35, 213-245 (1948) · Zbl 0034.23303
[13] May, R. M.: Stability and complexity in model ecosystems. 2nd ed. Princeton: Princeton Univ. Press 1974
[14] Parise, A.: Population dynamics and food supply in a Copepod of genus Tisbe. Boll. Zool. 45, 375-381 (1978)
[15] Rabinowitz, P. H.: Some global results for nonlinear eigenvalue problems. J. Functional Analysis 7, 487-513 (1971) · Zbl 0212.16504 · doi:10.1016/0022-1236(71)90030-9
[16] Rabinowitz, P. H.: Some aspects of nonlinear eigenvalue problems. Rocky Mountain J. Math. 3, 161-202 (1973) · Zbl 0255.47069 · doi:10.1216/RMJ-1973-3-2-161
[17] Volterra, V.: Leçons sur la théorie mathématique de la lutte pour la vie. Paris: Gauthier-Villars 1931
[18] Watt, K. E. F.: Ecology and resource management. New York: McGraw-Hill 1968 · Zbl 0162.46601
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