Global stability in difference equations satisfying the generalized Yorke condition |
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Authors: | Victor Tkachenko |
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Affiliation: | a Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivs'ka str. 3, Kiev, Ukraine b Instituto de Matemática y Fisica, Universidad de Talca, Casilla 747, Talca, Chile |
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Abstract: | We present several conditions sufficient for global stability of the zero solution of nonautonomous difference equation xn+1=qxn+fn(xn,…,xn−k), n∈Z, when the nonlinearities fn satisfy a sort of negative feedback condition. Moreover, for every k∈N, we indicate qk such that one of our stability conditions is sharp if q∈(0,qk]. We apply our results to discrete versions of Nicholson's blowflies equation, the Mackey-Glass equations, and the Wazewska and Lasota equation. |
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Keywords: | Difference equation Global stability Yorke condition Single species population models |
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