一个q变形的Logistic映射及其意义
A q-deformed logistic map and its implications
摘要：
提出了一种新的q-变形Logistic映射，并证明了它在部分x-空间中具有自相关性.得到了它的单圈和双圈非平凡不动点，这些不动点与通常的Logistic映射的不动点在定性和定量上都有区别。利用李雅普诺夫指数研究了所提出的q-逻辑斯蒂映射的稳定性，并通过改变变形参数q的值，可以从混沌状态转变为规则状态.这个q-逻辑地图上的Parrondo悖论的影响进行了检查。
英文摘要：
A new q-deformed logistic map is proposed and it is found to have concavity in parts of the x-space. Its one-cycle and two-cycle non-trivial fixed points are obtained which are found to be qualitatively and quantitatively different from those of the usual logistic map. The stability of the proposed q-logistic map is studied using Lyapunov exponent and with a change in the value of the deformation parameter q, one is able to go from the chaotic to regular dynamical regime. The implications of this q-logistic map on Parrondo's paradox are examined.
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