×
Chen, Diyi; Zhang, Runfan; Sprott, J. C.; Chen, Haitao; Ma, Xiaoyi

Synchronization between integer-order chaotic systems and a class of fractional-order chaotic systems via sliding mode control. (English) Zbl 1331.34129

Chaos 22, No. 2, 023130, 9 p. (2012).
Summary: In this paper, we focus on the synchronization between integer-order chaotic systems and a class of fractional-order chaotic system using the stability theory of fractional-order systems. A new sliding mode method is proposed to accomplish this end for different initial conditions and number of dimensions. More importantly, the vector controller is one-dimensional less than the system. Furthermore, three examples are presented to illustrate the effectiveness of the proposed scheme, which are the synchronization between a fractional-order Chen chaotic system and an integer-order T chaotic system, the synchronization between a fractional-order hyperchaotic system based on Chen’s system and an integer-order hyperchaotic system, and the synchronization between a fractional-order hyperchaotic system based on Chen’s system and an integer-order Lorenz chaotic system. Finally, numerical results are presented and are in agreement with theoretical analysis.{
©2012 American Institute of Physics}

Cited in 29 Documents

MSC:

34H10 Chaos control for problems involving ordinary differential equations
34H05 Control problems involving ordinary differential equations
34D06 Synchronization of solutions to ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
34A08 Fractional ordinary differential equations
93B51 Design techniques (robust design, computer-aided design, etc.)
34C60 Qualitative investigation and simulation of ordinary differential equation models
Cite Review PDF
Full Text: DOI

References:

[1] DOI: 10.1103/PhysRevLett.64.821 · Zbl 0938.37019 · doi:10.1103/PhysRevLett.64.821
[2] DOI: 10.1016/j.nonrwa.2010.10.009 · Zbl 1217.93061 · doi:10.1016/j.nonrwa.2010.10.009
[3] DOI: 10.1016/j.cnsns.2010.01.014 · doi:10.1016/j.cnsns.2010.01.014
[4] DOI: 10.1016/S0016-0032(97)00031-8 · Zbl 0892.58035 · doi:10.1016/S0016-0032(97)00031-8
[5] DOI: 10.1016/j.eswa.2010.01.022 · doi:10.1016/j.eswa.2010.01.022
[6] DOI: 10.1016/j.chaos.2010.10.002 · doi:10.1016/j.chaos.2010.10.002
[7] DOI: 10.1016/j.physleta.2005.10.101 · Zbl 1234.37055 · doi:10.1016/j.physleta.2005.10.101
[8] DOI: 10.1063/1.3072786 · Zbl 1311.93049 · doi:10.1063/1.3072786
[9] DOI: 10.1016/j.cnsns.2011.02.031 · Zbl 1219.93026 · doi:10.1016/j.cnsns.2011.02.031
[10] DOI: 10.1016/j.camwa.2011.04.010 · Zbl 1222.37106 · doi:10.1016/j.camwa.2011.04.010
[11] DOI: 10.1103/PhysRevE.80.026207 · doi:10.1103/PhysRevE.80.026207
[12] DOI: 10.1063/1.3515840 · Zbl 1311.34074 · doi:10.1063/1.3515840
[13] DOI: 10.1007/s11071-010-9813-4 · doi:10.1007/s11071-010-9813-4
[14] DOI: 10.1063/1.3383655 · Zbl 1311.37025 · doi:10.1063/1.3383655
[15] DOI: 10.1016/j.cnsns.2011.07.009 · Zbl 1239.93059 · doi:10.1016/j.cnsns.2011.07.009
[16] DOI: 10.1103/PhysRevE.81.041913 · doi:10.1103/PhysRevE.81.041913
[17] DOI: 10.1209/0295-5075/94/60007 · doi:10.1209/0295-5075/94/60007
[18] DOI: 10.1016/j.nonrwa.2011.05.006 · Zbl 1231.37020 · doi:10.1016/j.nonrwa.2011.05.006
[19] DOI: 10.1016/j.cnsns.2010.03.015 · Zbl 1221.93160 · doi:10.1016/j.cnsns.2010.03.015
[20] DOI: 10.1016/j.physleta.2010.10.038 · Zbl 1241.34088 · doi:10.1016/j.physleta.2010.10.038
[21] DOI: 10.1016/j.physa.2010.07.004 · doi:10.1016/j.physa.2010.07.004
[22] DOI: 10.1109/TCST.2009.2019120 · doi:10.1109/TCST.2009.2019120
[23] DOI: 10.1007/s11071-010-9904-2 · Zbl 1286.34016 · doi:10.1007/s11071-010-9904-2
[24] DOI: 10.1109/TFUZZ.2011.2127482 · doi:10.1109/TFUZZ.2011.2127482
[25] DOI: 10.1063/1.3629986 · Zbl 1318.34003 · doi:10.1063/1.3629986
[26] DOI: 10.1016/j.na.2009.10.033 · Zbl 1187.34066 · doi:10.1016/j.na.2009.10.033
[27] DOI: 10.1142/S021812741102874X · Zbl 1215.34072 · doi:10.1142/S021812741102874X
[28] DOI: 10.1007/s11071-011-0002-x · Zbl 1242.93027 · doi:10.1007/s11071-011-0002-x
[29] DOI: 10.1016/j.cnsns.2010.05.024 · Zbl 1221.34007 · doi:10.1016/j.cnsns.2010.05.024
[30] DOI: 10.1016/j.physa.2005.01.021 · doi:10.1016/j.physa.2005.01.021
[31] DOI: 10.1016/j.physleta.2006.06.021 · doi:10.1016/j.physleta.2006.06.021
[32] DOI: 10.1063/1.3068350 · Zbl 1311.34018 · doi:10.1063/1.3068350
[33] DOI: 10.2478/s13540-011-0029-1 · Zbl 1273.65101 · doi:10.2478/s13540-011-0029-1
[34] DOI: 10.1016/j.jmaa.2006.10.040 · Zbl 1113.37016 · doi:10.1016/j.jmaa.2006.10.040
[35] DOI: 10.1016/j.chaos.2009.03.092 · Zbl 1198.93020 · doi:10.1016/j.chaos.2009.03.092
[36] DOI: 10.1016/j.chaos.2004.02.035 · Zbl 1069.37025 · doi:10.1016/j.chaos.2004.02.035
[37] Zheng L. Y., Acta Phys. Sin. 56 pp 707– (2007)
[38] DOI: 10.1016/j.physleta.2009.04.063 · Zbl 1231.34091 · doi:10.1016/j.physleta.2009.04.063
[39] DOI: 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2 · Zbl 1417.37129 · doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.