A mathematical exploration into manipulation and control of a bifurcative dreaming process

Abstract

Mathematical models derived from the concepts of nonlinear dynamics and chaos theory for representing the highly nonrational transformations and bifurcations in a dreaming process may be highly useful for the study of dreams. In this work, three chaotic dynamical models known as the logistic map, sine map and cubic map have been adopted as a mathematical analogy for representing bifurcative dreaming processes. Further, the effect of a dream potentiator has been incorporated into the adopted models. For studying the effects of the dream potentiator on the actual dreaming process, computer simulations were performed. Results demonstrate that the dream potentiator may enhance the actual dream by elevating the dream states, by expanding the bifurcations and by reducing the number of successive steps required for attaining a dream state of deterministic chaos.