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A Simple Guide for Plotting a Proper Bifurcation Diagram

Health Technology Research Institute, Amirkabir University of Technology, No. 350, Hafez Ave, Valiasr Square, Tehran 159163-4311, Iran

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Iqtadar Hussain

Department of Mathematics, Statistics and Physics, Qatar University, Doha 2713, Qatar

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Fahimeh Nazarimehr

Department of Biomedical Engineering, Amirkabir University of Technology, No. 350, Hafez Ave, Valiasr Square, Tehran 159163-4311, Iran

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Seyed Mohammad Reza Hashemi Golpayegani

Department of Biomedical Engineering, Amirkabir University of Technology, No. 350, Hafez Ave, Valiasr Square, Tehran 159163-4311, Iran

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, and

Sajad Jafari

https://orcid.org/0000-0002-6845-7539

Health Technology Research Institute, Amirkabir University of Technology, No. 350, Hafez Ave, Valiasr Square, Tehran 159163-4311, Iran

Department of Biomedical Engineering, Amirkabir University of Technology, No. 350, Hafez Ave, Valiasr Square, Tehran 159163-4311, Iran

E-mail Address: sajadjafari@aut.ac.ir

Corresponding author.

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https://doi.org/10.1142/S0218127421500115Cited by:18 (Source: Crossref)

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.

Keywords:

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