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On disappearance of chaos in fractional systems

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  • Deshpande, Amey S.
  • Daftardar-Gejji, Varsha

Abstract

In a seminal paper, Grigorenko and Grigorenko [15], numerically studied fractional order dynamical systems (FODS) of the form Dαixi=fi(x1,x2,x3),0≤αi≤1,(i=1,2,3); and showed the existence of chaos in case of fractional Lorenz system when Σ=α1+α2+α3≤3. Since then voluminous numerical work has been done to explore various FODS, in this regard. It is now an established fact that Σ acts as a chaos controlling parameter.

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  • Deshpande, Amey S. & Daftardar-Gejji, Varsha, 2017. "On disappearance of chaos in fractional systems," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 119-126.
    • Handle: RePEc:eee:chsofr:v:102:y:2017:i:c:p:119-126
    DOI: 10.1016/j.chaos.2017.04.046
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    1. Sheu, Long-Jye & Chen, Hsien-Keng & Chen, Juhn-Horng & Tam, Lap-Mou & Chen, Wen-Chin & Lin, Kuang-Tai & Kang, Yuan, 2008. "Chaos in the Newton–Leipnik system with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 98-103.
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    3. Chen, Wei-Ching, 2008. "Nonlinear dynamics and chaos in a fractional-order financial system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1305-1314.
    4. Li, Chunguang & Chen, Guanrong, 2004. "Chaos and hyperchaos in the fractional-order Rössler equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 341(C), pages 55-61.
    5. Deng, W.H. & Li, C.P., 2005. "Chaos synchronization of the fractional Lü system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 353(C), pages 61-72.
    6. Xu, Beibei & Chen, Diyi & Zhang, Hao & Wang, Feifei, 2015. "Modeling and stability analysis of a fractional-order Francis hydro-turbine governing system," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 50-61.
    7. Deshpande, Amey S. & Daftardar-Gejji, Varsha & Sukale, Yogita V., 2017. "On Hopf bifurcation in fractional dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 189-198.
    8. Sheu, Long-Jye & Chen, Hsien-Keng & Chen, Juhn-Horng & Tam, Lap-Mou, 2007. "Chaos in a new system with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1203-1212.
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    1. Peng, Dong & Sun, Kehui & He, Shaobo & Alamodi, Abdulaziz O.A., 2019. "What is the lowest order of the fractional-order chaotic systems to behave chaotically?," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 163-170.

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