Krishnan Nair, P R; Nandakumaran, V M(Springer, October , 1998)
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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 > 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.