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.
| Original language | English |
|---|---|
| Pages (from-to) | 961-970 |
| Number of pages | 10 |
| Journal | Computers and Mathematics with Applications |
| Volume | 62 |
| Issue number | 3 |
| DOIs | |
| State | Published - Aug 2011 |
| Externally published | Yes |
Keywords
- Chaotic systems
- Chua's circuit
- Fractional differential equations
- Memristor
- Non-standard finite difference schemes
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