On disappearance of chaos in fractional systems

Amey S. Deshpande and Varsha Daftardar-Gejji

Chaos, Solitons & Fractals, 2017, vol. 102, issue C, 119-126

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.

Keywords: Fractional order; Dynamical systems; Caputo derivative; Chaos; Poincaré–Bendixon theorem (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:102:y:2017:i:c:p:119-126

DOI: 10.1016/j.chaos.2017.04.046

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