Stability and non-standard finite difference method of the generalized Chua's circuit

Handle URI:
http://hdl.handle.net/10754/561826
Title:
Stability and non-standard finite difference method of the generalized Chua's circuit
Authors:
Radwan, Ahmed G.; Moaddy, K.; Momani, Shaher M.
Abstract:
In this paper, we develop a framework to obtain approximate numerical solutions of the fractional-order Chua's circuit with Memristor using a non-standard finite difference method. Chaotic response is obtained with fractional-order elements as well as integer-order elements. Stability analysis and the condition of oscillation for the integer-order system are discussed. In addition, the stability analyses for different fractional-order cases are investigated showing a great sensitivity to small order changes indicating the poles' locations inside the physical s-plane. The GrnwaldLetnikov method is used to approximate the fractional derivatives. Numerical results are presented graphically and reveal that the non-standard finite difference scheme is an effective and convenient method to solve fractional-order chaotic systems, and to validate their stability. © 2011 Elsevier Ltd. All rights reserved.
KAUST Department:
Electrical Engineering Program; Physical Sciences and Engineering (PSE) Division
Publisher:
Elsevier BV
Journal:
Computers & Mathematics with Applications
Issue Date:
Aug-2011
DOI:
10.1016/j.camwa.2011.04.047
Type:
Article
ISSN:
08981221
Appears in Collections:
Articles; Physical Sciences and Engineering (PSE) Division; Electrical Engineering Program

Full metadata record

DC FieldValue Language
dc.contributor.authorRadwan, Ahmed G.en
dc.contributor.authorMoaddy, K.en
dc.contributor.authorMomani, Shaher M.en
dc.date.accessioned2015-08-03T09:31:50Zen
dc.date.available2015-08-03T09:31:50Zen
dc.date.issued2011-08en
dc.identifier.issn08981221en
dc.identifier.doi10.1016/j.camwa.2011.04.047en
dc.identifier.urihttp://hdl.handle.net/10754/561826en
dc.description.abstractIn this paper, we develop a framework to obtain approximate numerical solutions of the fractional-order Chua's circuit with Memristor using a non-standard finite difference method. Chaotic response is obtained with fractional-order elements as well as integer-order elements. Stability analysis and the condition of oscillation for the integer-order system are discussed. In addition, the stability analyses for different fractional-order cases are investigated showing a great sensitivity to small order changes indicating the poles' locations inside the physical s-plane. The GrnwaldLetnikov method is used to approximate the fractional derivatives. Numerical results are presented graphically and reveal that the non-standard finite difference scheme is an effective and convenient method to solve fractional-order chaotic systems, and to validate their stability. © 2011 Elsevier Ltd. All rights reserved.en
dc.publisherElsevier BVen
dc.subjectChaotic systemsen
dc.subjectChua's circuiten
dc.subjectFractional differential equationsen
dc.subjectMemristoren
dc.subjectNon-standard finite difference schemesen
dc.titleStability and non-standard finite difference method of the generalized Chua's circuiten
dc.typeArticleen
dc.contributor.departmentElectrical Engineering Programen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.identifier.journalComputers & Mathematics with Applicationsen
dc.contributor.institutionDepartment of Engineering Mathematics, Faculty of Engineering, Cairo University, Egypten
dc.contributor.institutionSchool of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Malaysiaen
dc.contributor.institutionDepartment of Mathematics, Faculty of Science, University of Jordan, Amman 11942, Jordanen
kaust.authorRadwan, Ahmed G.en
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