A novel chaotification scheme for fractional system and its application

Little seems to be known about the chaotification control of fractional order linear and nonlinear systems. This paper proposes a novel chaotification method for fractional order nonlinear systems based on the negative damping instability mechanism and fractional calculus technique. We then apply it...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 339; pp. 275 - 284
Main Authors Zhu, Huijian, Zeng, Caibin
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.09.2018
Subjects
Chaotification
Coexisting attractors
Fractional calculus
Lorenz system
34H10
Lorenz system
Chaotification
26A33
37D45
Fractional calculus
Coexisting attractors
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Summary:Little seems to be known about the chaotification control of fractional order linear and nonlinear systems. This paper proposes a novel chaotification method for fractional order nonlinear systems based on the negative damping instability mechanism and fractional calculus technique. We then apply it to chaotify the fractional order Lorenz system with order lying in (1,2), which is stable originally with specific parameters. Moreover, we introduce three critical effective orders to distinguish different four dynamics: singleton sets attractor, self-excited attractor, coexisting attractors, and blow up behavior. Many simulations are carried out to illustrate the effectiveness of the results. •A new method for chaotifying the fractional order nonlinear systems is proposed.•Fractional operator lying in (1, 2) has the negative damping instability effect.•Three critical orders are introduced to distinguish different complex dynamics.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2017.10.008