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Persistence of species obeying difference equations. (English) Zbl 0495.92015

92D25 Population dynamics (general)
91A40 Other game-theoretic models
39A10 Additive difference equations
92D40 Ecology
91A12 Cooperative games
39A12 Discrete version of topics in analysis
Full Text: DOI
[1] Albrecht F., Gatzke, H., Haddad, A., Wax, N.: The dynamics of two interacting populations. J. Math. Anal. Appl. 46, 658-670 (1974) · Zbl 0281.92012
[2] Brauer, F.: Boundedness of solutions of predator-prey systems. Theoret. Population Biology 15, 268-273 (1979) · Zbl 0399.92015
[3] Goh, B.: Management and analysis of biological populations. Amsterdam: Elsevier 1980
[4] Gumowski, I., Mira, C.: Recurrences and discrete dynamical systems. Lecture notes in Math., Vol. 809. Berlin: Springer 1980 · Zbl 0449.58003
[5] Hale, J.: Theory of functional differential equations. New York: Springer 1977 · Zbl 0352.34001
[6] Hasseil, M. P.: Anthropod predator-prey systems. Princeton, New Jersey: Princeton University Press 1978
[7] Hofbauer, J.: General cooperation theorem for hypercycles. Monatsh. Math. 91, 233-240 (1981) · Zbl 0449.34039
[8] Lasota, A.: Ergodic problems in biology. Asterisque 50, 239-250 (1977)
[9] Levin, S. A. (ed.): Ecosystem analysis and prediction. Proceedings of a SIAM-SIMS Conference held at Alta, Utah; 1974 (SIAM 1976) · Zbl 0298.00028
[10] Marotto, F. R.: Snap-back repellers imply chaos in ?n. J. Math. Anal. Appl. 63, 199-223 (1978) · Zbl 0381.58004
[11] May, R. M.: Biological populations with nonoverlapping generations: stable points, stable cycles, and chaos. Science 18, 645-647 (1974)
[12] May, R. M.: Nonlinear aspects of competition between three species. SIAM J. Appl. Math. 29, 243-253 (1975) · Zbl 0314.92008
[13] May, R. M., Oster, G. F.: Bifurcations and dynamic complexity in simple ecological models. American Naturalist 110, 573-599 (1976)
[14] Roughgarden, J.: Theory of population genetics and evolutionary ecology: An introduction. New York: MacMillan 1979
[15] Schuster, P., Sigmund, K., Wolff, R.: Dynamical systems under constant organization. III. Cooperative and competitive behaviour of hypercycles. J. Diff. Equns. 32, 357-368 (1979) · Zbl 0397.34055
[16] Smale, S., Williams, R. F.: The qualitative analysis of a difference equation of population growth. J. Math. Biol. 3, 1-4 (1976) · Zbl 0342.92014
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