Generalising the logistic map through the $q$-product

Details Generalising the logistic map through the $q$-product Generalising the logistic map through the $q$-product

2011-02-22

arxiv.org/abs/1102.4609v1

J. Phys.: Conference Series 285, 012042 (2011)

Nonlinear Sciences

Chaotic Dynamics

12 pages, 23 figures, Dynamics Days South America. To be published in Journal of Physics: Conference Series (JPCS - IOP)

Scientific paper

10.1088/1742-6596/285/1/012042

We investigate a generalisation of the logistic map as $ x_{n+1}=1-ax_{n}\otimes_{q_{map}} x_{n}$ ($-1 \le x_{n} \le 1$, $01$ at the edge of chaos, particularly at the first critical point $a_c$, that depends on the value of $q_{map}$. Bifurcation diagrams, sensitivity to initial conditions, fractal dimension and rate of entropy growth are evaluated at $a_c(q_{map})$, and connections with nonextensive statistical mechanics are explored.

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