On the dynamics of the \(q\)-deformed logistic map. (English) Zbl 1476.62268
Summary: We analyze the \(q\)-deformed logistic map, where the \(q\)-deformation follows the scheme inspired in the Tsallis \(q\)-exponential function. We compute the topological entropy of the dynamical system, obtaining the parametric region in which the topological entropy is positive and hence the region in which chaos in the sense of T.-Y. Li and J. A. Yorke [Am. Math. Mon. 82, 985–992 (1975; Zbl 0351.92021)] exists. In addition, it is shown the existence of the so-called Parrondo’s paradox where two simple maps are combined to give a complicated dynamical behavior.
MSC:
| 62P35 | Applications of statistics to physics |
| 62J12 | Generalized linear models (logistic models) |
| 54C70 | Entropy in general topology |
| 94A17 | Measures of information, entropy |
| 37C25 | Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics |
| 37N20 | Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) |
| 81P45 | Quantum information, communication, networks (quantum-theoretic aspects) |
Citations:
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