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Crossover Dynamics of Lorenz Model: Numerical Simulations |
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PP: 333-349 |
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doi:10.18576/pfda/110208
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Author(s) |
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Nasser Hassan Sweilam,
Seham Mahyoub Al-Mekhlafi,
Aya Refaat Mohamed,
Emad Mohamed Abo-Eldahab,
Assem Shawky Deif,
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Abstract |
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| In recent decades, there has been increased interest in the dynamic behaviors of fractional order differential systems. Many results on fractional-order chaotic systems were obtained only via analytical and numerical techniques. This paper aims to numerically study the demeanor of three different classes of piecewise chaotic systems. This system is Lorenz chaotic system. The fractional derivatives are defined in the Caputo and Riemann-Liouville senses. The deterministic model is expanded using the constant proportional Caupto operator. Gru ̈nwald−Letnikov non-standard finite difference scheme is presented to approximate the constant proportional Caupto fractional operator. Finally, numerical simulations are provided to confirm the accuracy of our research and provide comparison analyses.
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