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Sadeghi Bajestani G, Monzavi A, Hashemi Golpaygani S M R. Precisely chaotic models survey with Qualitative Bifurcation Diagram. JSDP 2016; 13 (3) :17-34
URL: http://jsdp.rcisp.ac.ir/article-1-309-en.html
Precisely chaotic models survey with Qualitative Bifurcation Diagram
Ghasem Sadeghi Bajestani * , Abbas Monzavi , Seyed Mohamad Reza Hashemi Golpaygani
Abstract:   (8442 Views)

The most important method  for behavior recognition of recurrent maps is to plot bifurcation diagram. In conventional method used for plotting bifurcation diagram,  a couple of time series for different values of model parameter have been generated and these points have been plotted with due respect to it after transient state. It does not have enough accuracy necessary for period detection and essential for discrimination between long periodic behaviors from chaotic behaviors; on the other hand because of being 2-dimensinal, it will not be possible to investigate the effect if the initial condition is in the basin of attraction.
In this research, a new bifurcation diagram is presented which is called: Qualitative Bifurcation Diagram (QBD). QBD provides accurate determination of periodicity. Results of our algorithm implementation on logistic map, represents its ability on determining long periods and period windows. Bifurcation diagram of logistic map does not obey mosaic tiling patterns (patterns that are created by arrangement not interaction) as a disciplinein addition to having the dynamic order. Some benefits of QBD are: long period discrimination, period window detection, computation time reduction, period presentation instead of amplitude show. In the  following we have an analytical survey to Lyapunov exponent – as a usual measurement tool for chaotic behavior – and important notes are expressed. Finally, Recurrent Quantification Analysis (RQA) and QBD are compared.  

Keywords: Bifurcation diagram, Chaos, Logistic Map, Lyapunov Exponent, Recurrent Quantification Analysis
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Type of Study: بنیادی | Subject: Paper
Received: 2015/01/3 | Accepted: 2016/09/7 | Published: 2017/04/23 | ePublished: 2017/04/23
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