Existence of multiple attractors and the nature of bifurcations in a discontinuous logistic map

We present the analytical investigations on a logistic map with a discontinuity at the centre. An explanation for the bifurcation phenomenon in discontinuous systems is presented. We establish that whenever the elements of an n-cycle (n > 1) approach the discontinuities of the nth iterate of the map, a bifurcation other than the usual period-doubling one takes place. The periods of the cycles decrease in an arithmetic progression, as the control parameter is varied. The system also shows the presence of multiple attractors. Our results are verified by numerical experiments as well.

Evidence for the existence of Sarkovskii ordering in a two-dimensional map

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.

Evidence for the existence of multiple equilibrium states in cobalt phthalocyanine tetramer: a study by dielectric spectroscopy

In any investigation, information about the molecules under consideration is very essential for tailoring their properties. Evaluation of dispersion parameters, namely optical dielectric constant, static dielectric constant, relaxation time and spreading factor, assumes significance in this context. Dielectric spectroscopy is a useful tool for estimating these parameters. Not only does it reveal details about these constants but it also gives insight into the mechanism of conduction. In this paper the evaluation of dispersion parameters of cobalt phthalocyanine tetramer in the temperature range 300–393K is attempted using Cole–Cole plots. The temperature variation of the spreading factor indicates the existence of multiple equilibrium positions in the case of cobalt phthalocyanine tetramer. To the best of our knowledge, the evaluation of dispersion parameters for cobalt phthalocyanine tetramer is reported for the first time