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Competition for fluctuating nutrient. (English) Zbl 0525.92024

92D25Population dynamics (general)
34C25Periodic solutions of ODE
Full Text: DOI
[1] Artstein, Z.: Limiting equations and stability of non-autonomous differential equations. Appendix A in J. P. LaSalle, The stability of dynamical systems, SIAM Regional Conf. Series in Applied Mathematics, no 25, SIAM, Philadelphia, 1976
[2] Hale, J. K.: Ordinary differential equations. Kreiger, 1980 · Zbl 0433.34003
[3] Hale, J. K.: Theory of functional differential equations. Berlin-Heidelberg-New York: Springer, 1977 · Zbl 0352.34001
[4] Hale, J. K.: Some recent results on dissipative processes. Lecture Notes in Math., vol. 799. Berlin-Heidelberg-New York: Springer, 1980 · Zbl 0433.34056
[5] Hirsch, M.: Systems of differential equations which are competitive or cooperative 1: Limit sets. SIAM J. Math. Anal. (1982) · Zbl 0494.34017
[6] Hirsch, M.: Systems of differential equations which are competitive or cooperative II: Convergence almost everywhere. (To appear) · Zbl 0658.34023
[7] Hsu, C. B.: A competition model for a seasonally fluctuating nutrient. J. Math. Biology 9, 115-132 (1980) · Zbl 0431.92027 · doi:10.1007/BF00275917
[8] Hsu, S. B.: Limiting behavior for competing species. SIAM J. Appl. Math. 34, 760-763 (1978) · Zbl 0381.92014 · doi:10.1137/0134064
[9] Hsu, S. B., Hubbell, S. P., Waltman, P. E.: A mathematical theory for single nutrient competition in continuous cultures of micro-organisms. SIAM J. of Appl. Math. 32, 366-383 (1977) · Zbl 0354.92033 · doi:10.1137/0132030
[10] LaSalle, J. P.: The stability of dynamical systems. Regional Conference Series in Applied Math. no 25, SIAM, Philadelphia, 1976 · Zbl 0364.93002
[11] Mottoni, P., de Schiaffino, A: Competition systems with periodic coefficients. A geometric approach. J. Math. Biol. 11, 319-335 (1981) · Zbl 0474.92015 · doi:10.1007/BF00276900
[12] Pliss, V. A.: Non local problems in the theory of oscillations. New York: Academic Press, Inc., 1966 · Zbl 0151.12104
[13] Pliss, V. A.: Integral manifolds for periodic systems of differential equations (Russian) Nauka. Moskva, 1977 · Zbl 0463.34002
[14] Smith, H. L.: Competitive coexistence in an oscillating chemostat. SIAM J. Appl. Math. 40 (No. 3) (1981). · Zbl 0467.92018
[15] Yoshizawa, T.: Stability theory by Liapunov’s second method. The Math. Society of Japan, 1966 · Zbl 0144.10802