Jacobian Matrix Algorithm for Lyapunov Exponents of the Discrete Fractional Maps
| dc.contributor.author | Baleanu, Dumitru | |
| dc.contributor.author | Wu, Guo-Cheng | |
| dc.date.accessioned | 2017-04-18T10:47:48Z | |
| dc.date.accessioned | 2025-09-18T12:08:46Z | |
| dc.date.available | 2017-04-18T10:47:48Z | |
| dc.date.available | 2025-09-18T12:08:46Z | |
| dc.date.issued | 2015 | |
| dc.description | Wu, Guo-Cheng/0000-0002-1946-6770 | en_US |
| dc.description.abstract | The Jacobian matrix algorithm is often used to calculate the Lyapunov exponents of the chaotic systems. This study extends the algorithm to discrete fractional cases. The tangent maps with memory effect are presented. The Lyapunov exponents of one and two dimensional fractional logistic maps are calculated. The positive ones are used to distinguish the chaotic areas of the maps. (C) 2014 Elsevier B.V. All rights reserved. | en_US |
| dc.description.sponsorship | National Natural Science Foundation of China [11301257]; Seed Funds for Major Science and Technology Innovation Projects of Sichuan Provincial Education Department [14CZ0026]; Innovative Team Program of the Neijiang Normal University [13TD01] | en_US |
| dc.description.sponsorship | This work was financially supported by the National Natural Science Foundation of China (Grant No. 11301257), the Seed Funds for Major Science and Technology Innovation Projects of Sichuan Provincial Education Department (Grant No. 14CZ0026) and the Innovative Team Program of the Neijiang Normal University (Grant No. 13TD01). The first author feels grateful to Prof. Yu Xue who gave sincere help when preparing the paper in the City University of Hongkong this summer. We also appreciate all the referees' kind suggestions. | en_US |
| dc.identifier.citation | Wu, G.C., Baleanu, D. (2015). Jacobian matrix algorithm for Lyapunov exponents of the discrete fractional maps. Communications In Nonlinear Science And Numerical Simulation, 22(1-3), 95-100. http://dx.doi.org/10.1016/j.cnsns.2014.06.042 | en_US |
| dc.identifier.doi | 10.1016/j.cnsns.2014.06.042 | |
| dc.identifier.issn | 1007-5704 | |
| dc.identifier.issn | 1878-7274 | |
| dc.identifier.scopus | 2-s2.0-85027943162 | |
| dc.identifier.uri | https://doi.org/10.1016/j.cnsns.2014.06.042 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12416/11217 | |
| dc.language.iso | en | en_US |
| dc.publisher | Elsevier | en_US |
| dc.relation.ispartof | Communications in Nonlinear Science and Numerical Simulation | |
| dc.rights | info:eu-repo/semantics/closedAccess | en_US |
| dc.subject | Discrete Fractional Calculus | en_US |
| dc.subject | Lyapunov Exponent | en_US |
| dc.subject | Symbolic Computation | en_US |
| dc.title | Jacobian Matrix Algorithm for Lyapunov Exponents of the Discrete Fractional Maps | en_US |
| dc.title | Jacobian matrix algorithm for Lyapunov exponents of the discrete fractional maps | tr_TR |
| dc.type | Article | en_US |
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| gdc.author.id | Wu, Guo-Cheng/0000-0002-1946-6770 | |
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| gdc.author.wosid | Baleanu, Dumitru/B-9936-2012 | |
| gdc.author.wosid | Wu, Guo-Cheng/T-9088-2017 | |
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| gdc.description.department | Çankaya University | en_US |
| gdc.description.departmenttemp | [Wu, Guo-Cheng] Neijiang Normal Univ, Coll Math & Informat Sci, Inst Appl Nonlinear Sci, Neijiang 641100, Peoples R China; [Baleanu, Dumitru] King Abdulaziz Univ, Fac Engn, Dept Chem & Mat Engn, Jeddah 21589, Saudi Arabia; [Baleanu, Dumitru] Inst Space Sci, Bucharest, Romania; [Baleanu, Dumitru] Cankaya Univ, Fac Arts & Sci, Dept Math & Comp Sci, TR-06530 Ankara, Turkey | en_US |
| gdc.description.endpage | 100 | en_US |
| gdc.description.issue | 1-3 | en_US |
| gdc.description.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
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| gdc.description.startpage | 95 | en_US |
| gdc.description.volume | 22 | en_US |
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| gdc.oaire.keywords | Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) | |
| gdc.oaire.keywords | Numerical nonlinear stabilities in dynamical systems | |
| gdc.oaire.keywords | discrete fractional calculus | |
| gdc.oaire.keywords | Lyapunov exponent | |
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