A statistical measure of complexity with nonextensive entropy

A statistical measure of complexity utilising the concept of entropy or information is proposed. Our way in this study is to use a nonextensive entropy instead of an extensive (additive) Shannon entropy in the definition, but can be characterised as a difference between the qth-order Renyi entropy and the second one. Furthermore, we devise a conditional, joint, and mutual complexity measure as a coherent possibility. The behavior of the measure for the logistic map shows that it is more sensitive to nonextensivity at the transition point a(c) similar to 3.8284... than any other values when 0 < q < 1. (C) 2004 Elsevier B.V. All rights reserved.