Journal of Pure and Applied Mathematics: Advances and ApplicationsAuthor's: HENA RANI BISWAS
Pages: [69] - [101]
Received Date: February 25, 2013; Revised April 12, 2013
Submitted by: Kh. Abdul Maleque.
In this paper, we studied basic dynamical facts of one-dimensional maps and their dynamical behaviour, especially chaotic behaviour of the maps. Using Lyapunov exponent in this work, it is found that logistic map, tent map, and doubling map are chaotic. We have shown that these maps are topological transitive and sensitive to initial condition. In this work, we have found that one-dimensional maps have complicated dynamical behaviour. We have solved some problems of tent map and after solving those problems, we illustrated that tent map is chaotic. We also discussed the bifurcation of one-dimensional map (logistic map) and sketch bifurcation diagrams by using Mathematica.
one-dimensional maps, topologically transitive, sensitive dependence on initial conditions, Lyapunov exponent, bifurcation.
