Design of Positive, Negative, and Alternating Sign Generalized Logistic Maps
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 chaoti...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/586783 |
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| _version_ | 1832567617052737536 |
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| author | Wafaa S. Sayed Ahmed G. Radwan Hossam A. H. Fahmy |
| author_facet | Wafaa S. Sayed Ahmed G. Radwan Hossam A. H. Fahmy |
| author_sort | Wafaa S. Sayed |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-c04c36f0f21744f9b213b92af57f7cab |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-c04c36f0f21744f9b213b92af57f7cab2025-02-03T01:01:08ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/586783586783Design of Positive, Negative, and Alternating Sign Generalized Logistic MapsWafaa S. Sayed0Ahmed G. Radwan1Hossam A. H. Fahmy2Engineering Mathematics and Physics Department, Faculty of Engineering, Cairo University, Giza 12613, EgyptEngineering Mathematics and Physics Department, Faculty of Engineering, Cairo University, Giza 12613, EgyptElectronics and Electrical Communications Department, Faculty of Engineering, Cairo University, Giza 12613, EgyptThe 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.http://dx.doi.org/10.1155/2015/586783 |
| spellingShingle | Wafaa S. Sayed Ahmed G. Radwan Hossam A. H. Fahmy Design of Positive, Negative, and Alternating Sign Generalized Logistic Maps Discrete Dynamics in Nature and Society |
| title | Design of Positive, Negative, and Alternating Sign Generalized Logistic Maps |
| title_full | Design of Positive, Negative, and Alternating Sign Generalized Logistic Maps |
| title_fullStr | Design of Positive, Negative, and Alternating Sign Generalized Logistic Maps |
| title_full_unstemmed | Design of Positive, Negative, and Alternating Sign Generalized Logistic Maps |
| title_short | Design of Positive, Negative, and Alternating Sign Generalized Logistic Maps |
| title_sort | design of positive negative and alternating sign generalized logistic maps |
| url | http://dx.doi.org/10.1155/2015/586783 |
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