Open AccessDesign and implementation of grid multi-scroll fractional-order chaotic attractors
Author(s) -
Liping Chen,
Pan Wei,
Ranchao Wu,
J. A. Tenreiro Machado,
António M. Lopes
Publication year - 2016
Publication title -
chaos an interdisciplinary journal of nonlinear science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.971
H-Index - 113
eISSN - 1089-7682
pISSN - 1054-1500
DOI - 10.1063/1.4958717
Subject(s) - attractor , phase portrait , lyapunov exponent , chaotic , nonlinear system , equilibrium point , control theory (sociology) , mathematics , fractional order system , function (biology) , stability (learning theory) , computer science , topology (electrical circuits) , mathematical analysis , bifurcation , fractional calculus , physics , differential equation , control (management) , quantum mechanics , artificial intelligence , evolutionary biology , biology , machine learning , combinatorics
This paper proposes a novel approach for generating multi-scroll chaotic attractors in multidirections
for fractional-order (FO) systems. The stair nonlinear function series and the saturated
nonlinear function are combined to extend equilibrium points with index 2 in a new FO linear system.
With the help of stability theory of FO systems, stability of its equilibrium points is analyzed,
and the chaotic behaviors are validated through phase portraits, Lyapunov exponents, and Poincaré
section. Choosing the order 0.96 as an example, a circuit for generating 2-D grid multiscroll chaotic
attractors is designed, and 2-D 9x9 grid FO attractors are observed at most. Numerical simulations
and circuit experimental results show that the method is feasible and the designed circuit is correct.info:eu-repo/semantics/publishedVersio
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