A q-deformed nonlinear map

A scheme of q-deformation of nonlinear maps is introduced. As a specific example, a q-deformation procedure related to the Tsallis q-exponential function is applied to the logistic map. Compared to the canonical logistic map, the resulting family of q-logistic maps is shown to have a wider spectrum of interesting behaviours, including the co-existence of attractors -- a phenomenon rare in one dimensional maps.Comment: 17 pages, 19 figure

Mathematical Modelling and Didactics Sequences: a relationship of complementarity

The mathematical modelling has been presented in literature as an efficient way of contextualizing of elementary mathematical concepts, and as a possibility to the students living a researcher experience. But its use as a mathematic teaching method still presents questions to be explained from the educational point of view. This article analyses two kinds of use of modelling on the teaching, and treats the possible teaching results: as a part of a didactic sequence and as a didactic sequence generated from a real problem. The conclusions consider that the teaching resultant of didactic sequences of modelling is: an integrator of concepts and develops the ability to associate the mathematical concepts to the real situations; the teaching is, in a general analysis, incomplete when relationed to the learning of planned contents, needing other didactics sequences; and the modelling, when is complemented with didactic sequences, contributes to a more significant learning, without losing its characteristic of investigation of problems.213013114