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Volume 5, Number 2, 2015, Pages 210-219                                                                DOI:10.11948/2015019
Bifurcations and synchronization of the fractional-order simplified Lorenz hyperchaotic systems
Yan Wang,Shaobo He,Huihai Wang,Kehui Sun
Keywords:Fractional-order calculus, chaos, simplifed Lorenz hyperchaotic system, bifurcation, synchronization performance, active control.
      In this paper, dynamics of the fractional-order simplied Lorenz hyperchaotic system is investigated. Modied Adams-Bashforth-Moulton method is applied for numerical simulation. Chaotic regions and periodic windows are identied. Dierent types of motions are shown along the routes to chaos by means of phase portraits, bifurcation diagrams, and the largest Lyapunov exponent. The lowest fractional order to generate chaos is 3.8584. Synchronization between two fractional-order simplied Lorenz hyperchaotic systems is achieved by using active control method. The synchronization performances are studied by changing the fractional order, eigenvalues and eigenvalue standard deviation of the error system.
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