On some generalized discrete logistic maps
Recently, conventional logistic maps have been used in different vital applications like modeling and security. However, unfortunately the conventional logistic maps can tolerate only one changeable parameter. In this paper, three different generalized logistic maps are introduced with arbitrary pow...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2013-03-01
|
| Series: | Journal of Advanced Research |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S209012321200032X |
| _version_ | 1818964352850460672 |
|---|---|
| author | Ahmed G. Radwan |
| author_facet | Ahmed G. Radwan |
| author_sort | Ahmed G. Radwan |
| collection | DOAJ |
| description | Recently, conventional logistic maps have been used in different vital applications like modeling and security. However, unfortunately the conventional logistic maps can tolerate only one changeable parameter. In this paper, three different generalized logistic maps are introduced with arbitrary powers which can be reduced to the conventional logistic map. The added parameter (arbitrary power) increases the degree of freedom of each map and gives us a versatile response that can fit many applications. Therefore, the conventional logistic map is considered only a special case from each proposed map. This new parameter increases the flexibility of the system, and illustrates the performance of the conventional system within any required neighborhood. Many cases will be illustrated showing the effect of the arbitrary power and the equation parameter on the number of equilibrium points, their locations, stability conditions, and bifurcation diagrams up to the chaotic behavior. |
| first_indexed | 2024-12-20T12:59:45Z |
| format | Article |
| id | doaj.art-b8791c90f4874d3184eede560b00f0b2 |
| institution | Directory Open Access Journal |
| issn | 2090-1232 2090-1224 |
| language | English |
| last_indexed | 2024-12-20T12:59:45Z |
| publishDate | 2013-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Journal of Advanced Research |
| spelling | doaj.art-b8791c90f4874d3184eede560b00f0b22022-12-21T19:39:57ZengElsevierJournal of Advanced Research2090-12322090-12242013-03-014216317110.1016/j.jare.2012.05.003On some generalized discrete logistic mapsAhmed G. RadwanRecently, conventional logistic maps have been used in different vital applications like modeling and security. However, unfortunately the conventional logistic maps can tolerate only one changeable parameter. In this paper, three different generalized logistic maps are introduced with arbitrary powers which can be reduced to the conventional logistic map. The added parameter (arbitrary power) increases the degree of freedom of each map and gives us a versatile response that can fit many applications. Therefore, the conventional logistic map is considered only a special case from each proposed map. This new parameter increases the flexibility of the system, and illustrates the performance of the conventional system within any required neighborhood. Many cases will be illustrated showing the effect of the arbitrary power and the equation parameter on the number of equilibrium points, their locations, stability conditions, and bifurcation diagrams up to the chaotic behavior.http://www.sciencedirect.com/science/article/pii/S209012321200032XLogistic mapBifurcation diagramStabilityGeneralized 1D mapArbitrary powerChaos |
| spellingShingle | Ahmed G. Radwan On some generalized discrete logistic maps Journal of Advanced Research Logistic map Bifurcation diagram Stability Generalized 1D map Arbitrary power Chaos |
| title | On some generalized discrete logistic maps |
| title_full | On some generalized discrete logistic maps |
| title_fullStr | On some generalized discrete logistic maps |
| title_full_unstemmed | On some generalized discrete logistic maps |
| title_short | On some generalized discrete logistic maps |
| title_sort | on some generalized discrete logistic maps |
| topic | Logistic map Bifurcation diagram Stability Generalized 1D map Arbitrary power Chaos |
| url | http://www.sciencedirect.com/science/article/pii/S209012321200032X |
| work_keys_str_mv | AT ahmedgradwan onsomegeneralizeddiscretelogisticmaps |