A Simple Guide for Plotting a Proper Bifurcation Diagram
Ali Asghar Jafari, Iqtadar Hussain, Fahimeh Nazarimehr, Seyed Mohammad Reza Hashemi Golpayegani, Sajad Jafari
Abstract
In this paper, we propose a guideline for plotting the bifurcation diagrams of chaotic systems. We discuss numerical and mathematical facts in order to obtain more accurate and more elegant bifurcation diagrams. The importance of transient time and the phenomena of critical slowing down are investigated. Some critical issues related to multistability are discussed. Finally, a solution for fast obtaining an accurate sketch of the bifurcation diagram is presented. The solution is based on running the system for only one sample in each parameter value and using the system’s state in the previous value of the parameter as the initial condition.