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Nonlinear dynamics; logistic map; q-deformation; Tsallis statistics

Motivated by studies onq-deformed physical systems related to quantum group structures, and by the elements of Tsallis statistical mechanics, the concept ofq-deformed nonlinear maps is introduced. As a specific example, aq-deformation procedure is applied to the logistic map. Compared to the canonical logistic map, the resulting family ofq-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.

Ramaswamy Jaganathan¹ Sudeshna Sinha¹

1. The Institute of Mathematical Sciences, C.I.T. Campus, Tharamani, Chennai - 600 113, India

Published

March 2005