Design of Positive, Negative, and Alternating Sign Generalized Logistic Maps

Wafaa S. Sayed, Ahmed G. Radwan and Hossam A. H. Fahmy

Discrete Dynamics in Nature and Society, 2015, vol. 2015, 1-23

Abstract:

The discrete logistic map is one of the most famous discrete chaotic maps which has widely spread applications. This paper investigates a set of four generalized logistic maps where the conventional map is a special case. The proposed maps have extra degrees of freedom which provide different chaotic characteristics and increase the design flexibility required for many applications such as quantitative financial modeling. Based on the maximum chaotic range of the output, the proposed maps can be classified as positive logistic map, mostly positive logistic map, negative logistic map, and mostly negative logistic map. Mathematical analysis for each generalized map includes bifurcation diagrams relative to all parameters, effective range of parameters, first bifurcation point, and the maximum Lyapunov exponent (MLE). Independent, vertical, and horizontal scales of the bifurcation diagram are discussed for each generalized map as well as a new bifurcation diagram related to one of the added parameters. A systematic procedure to design two-constraint logistic map is discussed and validated through four different examples.

Date: 2015
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://downloads.hindawi.com/journals/DDNS/2015/586783.pdf (application/pdf)
http://downloads.hindawi.com/journals/DDNS/2015/586783.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:586783

DOI: 10.1155/2015/586783

Access Statistics for this article

More articles in Discrete Dynamics in Nature and Society from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().