Bifurcation Diagram of a Map with Multiple Critical Points

Abstract

In this work a conjecture to draw the bifurcation diagram of a map with multiple critical points is enunciated. The conjecture is checked by using two quartic maps in order to verify that the bifurcation diagrams obtained according to the conjecture contain all the periodic orbits previously counted by Xie and Hao for maps with four laps. We show that a map with split bifurcation contains more periodic orbits than those counted by these authors for a map with the same number of laps.

Predicting Tipping Points in Chaotic Maps with Period‐Doubling Bifurcations

“…e finite precision of computers has a significant effect on the simulation of chaotic dynamics [18]. Critical points of the bifurcation diagram in a chaotic map were investigated in [19]. Chaotic maps have some engineering applications, such as random number generators [20,21].…”