STUDY OF BIFURCATION AND HYPERBOLICITY IN DISCRETE DYNAMICAL SYSTEMS

Authors

1 Mathematical Sciences Foundation, N-91, Greater Kailash I, New Delhi-110048, India

2 Shyam Lal College (Evening), University of Delhi, Delhi-110032, India

3 Deparment of Mathematics, University of Delhi, Delhi-110007, India

Abstract

Bifurcations leading to chaos have been investigated in a number of one dimensional dynamical
systems by varying the parameters incorporated within the systems. The property hyperbolicity has been studied in detail in each case which has significant characteristic behaviours for regular and chaotic evolutions. In the process, the calculations for invariant set have also been carried out. A broad analysis of bifurcations and hyperbolicity provide some interesting results. The fractal property, self-similarity, has also been observed for chaotic regions within the bifurcation diagram. The results of numerical calculations assume significant values.

Keywords

Iranian Journal of Science
Volume 34, Issue 1 - Serial Number 1
January and February 2010
Pages 1-12

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