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

Ahmed G. Radwan, K. Moaddy, Shaher M. Momani

Research output: Contribution to journalArticlepeer-review

60 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)961-970
Number of pages10
JournalComputers & Mathematics with Applications
Volume62
Issue number3
DOIs
StatePublished - Aug 2011

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

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