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Existence of Multiple Attractors and the Nature of Bifurcations in a Discontinuous Logistic Map

Publication Type : Journal Article

Publisher : Springer

Source : Pramana, Springer, Volume 51, Number 3-4, p.377–385 (1998)

Campus : Amritapuri

School : School of Arts and Sciences

Department : Physics

Year : 1998

Abstract : 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 I) 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.

Cite this Research Publication : P. R. Krishnan Nair and Dr. V . M. Nandakumaran, “Existence of multiple attractors and the nature of bifurcations in a discontinuous logistic map”, Pramana, vol. 51, pp. 377–385, 1998

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