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Global dynamics of some periodically forced, monotone difference equations. (English) Zbl 1002.39003
This paper is concerned with the recurrence relation $x_{t+1}= x_tf\left( {x_t\over 1+\alpha (-1)^t}\right), \quad t=0,1,2, \dots; \alpha\in [0,1),$ there it is asumed that the function $$h(x)= xf(x)$$ is (roughly) smooth, positive, increasing and concave on $$[0,\infty)$$. Conditions under which there exist a globally attracting equilibrium or a globally attracting two cycle are given. Conditions under which attracting two cycles are attenuant are also given. Here, a two cycle $$(c_0,c_1)$$ is attenuant if the average $$(c_0+ c_1)/2$$ is less than the positive fixed point of $$x=h(x)$$.

##### MSC:
 39A11 Stability of difference equations (MSC2000) 92D25 Population dynamics (general)
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