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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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