Publication Type : Journal Article
Publisher : Elsevier
Source : Physics Letters A, vol. 142, pp. 483–489, 1989
Url : http://www.sciencedirect.com/science/article/pii/0375960189905197
Campus : Amritapuri
School : School of Arts and Sciences
Department : Physics
Year : 1989
Abstract : This is a sequel to our earlier work on the modulated logistic map. Here, we first show that the map comes under the universality class of Feigenbaum. We then give evidence for the fact that our model can generate strange attractors in the unit square for an uncountable number of parameter values in the range μ∞μ1. Numerical plots of the attractor for several values of μ are given and the self-similar structure is explicity shown in one case. The fractal and information dimensions of the attractors for many values of μ are shown to be greater than one and the variation in their structure is analysed using the two Lyapunov exponents of the system. Our results suggest that the map can be considered as an analogue of the logistic map in two dimensions and may be useful in describing certain higher dimensional chaotic phenomena.
Cite this Research Publication : K. P. Harikrishnan and Dr. V . M. Nandakumaran, “An analogue of the logistic map in two dimensions”, Physics Letters A, vol. 142, pp. 483–489, 1989