NEIMARK-SACKER BIFURCATION IN DELAYED LOGISTIC MAP

The purpose of this paper is to investigate the Neimark-Sacker bifurcation in delayed logistic map. In Neimark-Sacker bifurcation, the fixed point gets converted to a unit circle. In case of our considered map, we observed mode locked state near Neimark-Sacker bifurcation point. Using the analytical technique of Normal form, we have determined the mode locked state in the vicinity of the NS bifurcation point. We have also used numerical tools like final state diagram, Lyapunov exponent, phase portrait and time series plot to establish the transition from periodic to quasiperiodic through mode locked state and finally to chaotic state.