Geodesic
On cycles of a discrete periodic logistic equation
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 2, pp. 154-157
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For the discrete logistic equation $x_{k+1}=x_k\exp(r_k(1-x_k))$, $k\in Z_+$, where $\{r_k\}$ is a positive $n$-periodic sequence, it is shown that, under the condition $\prod^{n-1}_{k=0}(1-r_k)>1$, the equation has at least two positive $n$-cycles distinct from the equilibrium. Examples are considered.
Keywords: logistic equation, stability
Mots-clés : cycles, equilibria. 
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A. V. Lasunskii. On cycles of a discrete periodic logistic equation. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 2, pp. 154-157. http://geodesic.mathdoc.fr/item/TIMM_2010_16_2_a12/

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