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| 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∞<μ<1. 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. |
| URI: | http://dyuthi.cusat.ac.in/purl/2567 |
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| Dyuthi-P0126.pdf | (484.3Kb) |
| Abstract: | We have studied the bifurcation structure of the logistic map with a time dependant control parameter. By introducing a specific nonlinear variation for the parameter, we show that the bifurcation structure is modified qualitatively as well as quantitatively from the first bifurcation onwards. We have also computed the two Lyapunov exponents of the system and find that the modulated logistic map is less chaotic compared to the logistic map. |
| URI: | http://dyuthi.cusat.ac.in/purl/2562 |
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| Dyuthi-P0121.pdf | (521.1Kb) |
| Abstract: | We analyse numerically the bifurcation structure of a two-dimensional noninvertible map and show that different periodic cycles are arranged in it exactly in the same order as in the case of the logistic map. We also show that this map satisfies the general criteria for the existence of Sarkovskii ordering, which supports our numerical result. Incidently, this is the first report of the existence of Sarkovskii ordering in a two-dimensional map. |
| URI: | http://dyuthi.cusat.ac.in/purl/2569 |
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| Dyuthi-P0128.pdf | (408.6Kb) |
| Abstract: | We study the period-doubling bifurcations to chaos in a logistic map with a nonlinearly modulated parameter and show that the bifurcation structure is modified significantly. Using the renormalisation method due to Derrida et al. we establish the universal behaviour of the system at the onset of chaos. |
| URI: | http://dyuthi.cusat.ac.in/purl/2571 |
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| Dyuthi-P0130.pdf | (215.1Kb) |
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