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Competition for fluctuating nutrient. (English) Zbl 0525.92024

MSC:
92D40 Ecology
92D25 Population dynamics (general)
34C25 Periodic solutions to ordinary differential equations
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[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
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[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
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[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
[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
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