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Stability and non-standard finite difference method of the generalized Chua’s circuit
A.G. Radwan, K. Moaddy,
Published in Elsevier BV
2011
Volume: 62
   
Issue: 3
Pages: 961 - 970
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.
About the journal
JournalData powered by TypesetComputers and Mathematics with Applications
PublisherData powered by TypesetElsevier BV
ISSN08981221
Open AccessNo