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Synchronization of two coupled fractional-order chaotic oscillators. (English) Zbl 1077.70013
The authors study the master-slave synchronization of coupled fractional order chaotic oscillators. The authors find that two fractional-order chaotic oscillators can be brought to an exact synchronization with appropriate coupling strength. As the increasing of system order, the process of synchronization of two coupled fractional order \((q>3)\) oscillators can be smooth and stable.

70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics
26A33 Fractional derivatives and integrals
Full Text: DOI
[1] Bagley, R.L.; Calico, R.A., Fractional order state equations for the control of viscoelastically damped structures, J guidance, control dynamics, 14, 2, 304-311, (1991)
[2] Ichise, M.; Nagayanagi, Y.; Kojima, T., An analog simulation of noninteger order transfer functions for analysis of electrode processes, J electroanal chem interfacial electrochem, 33, 253-265, (1971)
[3] Heaviside, O., Electromagnetic theory, (1971), Chelsea New York · JFM 30.0801.03
[4] Hartly, T.T; Lorenzo, C.F.; Qammer, H.K., Chaos in a fractional order chua’s system, IEEE trans CAS-I, 42, 8, 485-490, (1995)
[5] Ahmad, W.; Ei-Khazali, R.; Elwakil, A.S., Fractional order wien-bridge oscillator, Electron lett, 37, 18, 1110-1112, (2001)
[6] Li, C.G.; Chen, G.R., Chaos and hyperchaos in the fractional-order rossler equations, Physica A, 341, 55-61, (2004)
[7] Ahmad, W.M.; Sprott, J.C., Chaos in fractional-order autonomous nonlinear systems, Chaos, solitons and fractals, 16, 339-351, (2003) · Zbl 1033.37019
[8] Li, C.G.; Chen, G.R., Chaos in the fractional-order Chen system and its control, Chaos, solitons and fractals, 22, 549-554, (2004) · Zbl 1069.37025
[9] Ahmad, W.M.; Harb, A.M., On nonlinear control design for autonomous chaotic systems of integer and fractional orders, Chaos, solitons and fractals, 18, 693-701, (2003) · Zbl 1073.93027
[10] Pecora, L.M.; Carrol, T.L.; Pecora, L.M.; Carrol, T.L., Driving systems with chaotic signals, Phys rev lett, Phys rev A, 44, 2374-2383, (1991)
[11] Podlubny, I., Fractional differential equations, (1999), Academic Press San Diego, CA · Zbl 0918.34010
[12] Charef, A.; Sun, H.H.; Tsao, Y.Y.; Onaral, B., Fractal system as represented by singularity function, IEEE trans automatic control, 37, 9, 1465-1470, (1992) · Zbl 0825.58027
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