TY - JOUR
T1 - Stability and non-standard finite difference method of the generalized Chua's circuit
AU - Radwan, Ahmed G.
AU - Moaddy, K.
AU - Momani, Shaher M.
N1 - KAUST Repository Item: Exported on 2020-10-01
PY - 2011/8
Y1 - 2011/8
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/561826
UR - https://linkinghub.elsevier.com/retrieve/pii/S0898122111003506
UR - http://www.scopus.com/inward/record.url?scp=79960983234&partnerID=8YFLogxK
U2 - 10.1016/j.camwa.2011.04.047
DO - 10.1016/j.camwa.2011.04.047
M3 - Article
SN - 0898-1221
VL - 62
SP - 961
EP - 970
JO - Computers & Mathematics with Applications
JF - Computers & Mathematics with Applications
IS - 3
ER -