Bifurcation analysis of logistic map using four step feedback procedure

Abstract

The logistic map occupies a renowned place in the dynamics of chaos theory and in diverse areas of science. Picard orbit and Superior orbit (Mann orbit) have been used to control this discrete chaotic dynamical system. In this article, we further extend the analytical study of logistic map using a four step feedback procedure (SP orbit). The dynamical properties such as fixed point, range of convergence and stability, periodicity and chaos of the logistic map have been investigated. These properties are illustrated experimentally by adopting dynamical techniques like fixed point analysis and bifurcation plot. Using this approach, one can easily control the chaotic system and make the system stable for higher values of population growth parameter r by selecting the control parameters carefully.