De Mottoni, Piero; Schiaffino, Andrea Competition systems with periodic coefficients: A geometric approach. (English) Zbl 0474.92015 J. Math. Biol. 11, 319-335 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 4 ReviewsCited in 112 Documents MSC: 92D25 Population dynamics (general) 34C25 Periodic solutions to ordinary differential equations 34D05 Asymptotic properties of solutions to ordinary differential equations 37-XX Dynamical systems and ergodic theory Keywords:two-species competition system; Volterra competition systems; periodic environment; violation of competitive exclusion; global properties; asymptotic behavior of non-negative solutions; Poincare map; Cauchy problem; domains of attraction; numerical computations; graphical representations PDF BibTeX XML Cite \textit{P. De Mottoni} and \textit{A. Schiaffino}, J. Math. Biol. 11, 319--335 (1981; Zbl 0474.92015) Full Text: DOI OpenURL References: [1] Bardi, M.: Predator-prey models in periodic environments. University of Padua: Preprint 1980 · Zbl 0466.92019 [2] 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 [3] Cushing, J. M.: Periodic time-dependent predator-prey systems. SIAM J. Appl. Math. 32, 82-95 (1977) · Zbl 0348.34031 [4] Cushing, J. M.: Two species competition in a periodic environment. J. Math. Biol. 10, 385-400 (1980) · Zbl 0455.92012 [5] Koch, A. L.: Coexistence resulting from an alternation of density dependent and density independent growth, J. Theor. Biol. 44, 373-386 (1974) [6] Krasnosel’skii, M. A.: The operator of translation along the trajectories of differential equations. Providence, RI: AMS 1968 [7] de Mottoni, P., Schiaffino, A.: On logistic equations with time periodic coefficients. Roma: Pubbl. IAC n. 192, 1979 · Zbl 0585.34031 [8] Pliss, V. A.: Integral’nye mno?estva periodi?eskih sistem differencial’nyh uravnenii. Moskva: Nauka 1977 (Russian) [9] Rosenblat, S.: Population models in a periodically fluctuating environment. J. Math. Biol. 9, 23-36 (1980) · Zbl 0426.92018 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.