The Characteristic Behavior and Bifurcation of the Cubic Map

Abstract

Important characteristics preserved from the standard 1-dimensional cubic map are studied here. Many important features of the original 1-dimensional cubic map have survived, and their behavior is being studied here. Attracting, repelling, and neutral fixed points are analyzed. The use of the map as an aid in the study of period doubling bifurcation has been depicted. On the other hand, map can display an exorbitance of additional behaviors. It can be seen that nearby spots on trajectories move closer together and further apart as time progresses. These are the paths that never seem to settle into regular orbits or stop moving altogether. Modifying the starting conditions even slightly can shift the course of evolution. In reality, patterns drive chaotic systems despite their seemingly nonlinear and unpredictable behavior. Exploring the chaotic behavior of the cubic equation by varying the governing parameters, finding Bifurcation diagrams, etc., are all subtopics of this work, but finding the cubic map is the main focus.

Jagannath University Journal of Science, Volume 10, Number I, Jun 2023, pp. 27-42