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  • Artikel  (2)
  • Ecology
  • crystal structure
  • 1980-1984  (2)
  • Mathematik  (2)
  • Geologie und Paläontologie
  • 1
    Digitale Medien
    Digitale Medien
    Springer
    Journal of mathematical biology 12 (1981), S. 343-354 
    ISSN: 1432-1416
    Schlagwort(e): Ecology ; Periodic differential equations ; Optimization
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Summary The theory developed here applies to populations whose size x obeys a differential equation, $$\dot x = r(t)xF(x,t)$$ in which r and F are both periodic in t with period p. It is assumed that the function r, which measures a population's intrinsic rate of growth or intrinsic rate of adjustment to environmental change, is measurable and bounded with a positive lower bound. It is further assumed that the function F, which is determined by the density-dependent environmental influences on growth, is such that there is a closed interval J, with a positive lower bound, in which there lies, for each t, a number K(t) for which $$F(K(t),t) = 0$$ and, as functions on J × ℝ, F is continuous, while ∂F/∂x is continuous, negative, and bounded. Because x(t) = 0, 〉 0, or 〈 0 in accord with whether K(t) = x(t), K(t) 〉 x(t), or K(t) 〈 x(t), the number K(t) is called the “carrying capacity of the environment at time t”. The assumptions about F imply that the number K(t) is unique for each t, depends continuously and periodically on t with period P, and hence attains its extrema, K min and K max. It is, moreover, easily shown that the differential equation for x has precisely one solution x * which has its values in J and is bounded for all t in ℝ; this solution is of period p, is asymptotically stable with all of J in its domain of attraction, and is such that its minimum and maximum values, x min * and x max * , obey $$K_{min} \leqslant x_{min}^* \leqslant x_{max}^* \leqslant K_{max}^* .$$ The following question is discussed: If the function F is given, and the function r can be chosen, which choices of r come close to maximizing, x min * ? The results obtained yield a procedure for constructing, for each F and each ɛ 〉 0, a function r such that x min * 〉 K max − ɛ.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
    BibTip Andere fanden auch interessant ...
  • 2
    Digitale Medien
    Digitale Medien
    Springer
    Journal of mathematical biology 18 (1983), S. 255-280 
    ISSN: 1432-1416
    Schlagwort(e): Population dyamics ; Ecology ; Periodic solutions
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A model of the competition of n species for a single essential periodically fluctuating nutrient is considered. Instead of the familiar Michaelis-Menten kinetics for nutrient uptake, we assume only that the uptake rate functions are positive, increasing and bounded above. Sufficient conditions for extinction are given. The existence of a nutrient threshold under which the Principle of Competitive Exclusion holds, is proven. For two species systems the following very general result is proven: All solutions of a τ-periodic, dissipative, competitive system are either τ-periodic or approach a τ-periodic solution. A complete description of the geometry of the Poincaré operator of the two species system is given.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
    BibTip Andere fanden auch interessant ...
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