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А.В. Ласунский.
О периоде решений дискретного периодического логистического уравнения
// Труды КарНЦ РАН. No 5. Сер. Математическое моделирование и информационные технологии. Вып. 3. 2012. C. 44-48
A.V. Lasunsky. On the period of solutions of a discrete periodic logistic equation // Transactions of Karelian Research Centre of Russian Academy of Science. No 5. Mathematical Modeling and Information Technologies. Vol. 3. 2012. Pp. 44-48
Keywords: discrete periodic logistic equation, period of solution, stability
It is shown that the discrete periodic logistic equation
xn+1 = xnexp (rn (1 - xn))
with a positive ω-periodic coefficient rn (ω ≠ 1) cannot have Ω -periodic solutions (Ω ≠1) with the period coprime to ω. A discrete analog of the Massera-Kurzweil theorem was obtained. Examples of the ω-periodic logistic equation with periodic solutions of the period ω; 2 ω; 3 ω were constructed using a computer program. The solutions are examined for stability.
xn+1 = xnexp (rn (1 - xn))
with a positive ω-periodic coefficient rn (ω ≠ 1) cannot have Ω -periodic solutions (Ω ≠1) with the period coprime to ω. A discrete analog of the Massera-Kurzweil theorem was obtained. Examples of the ω-periodic logistic equation with periodic solutions of the period ω; 2 ω; 3 ω were constructed using a computer program. The solutions are examined for stability.
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Last modified: November 21, 2012