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Volumn 74, Issue 4, 2013, Pages 1169-1181

Feedback synchronization of the fractional order reverse butterfly-shaped chaotic system and its application to digital cryptography

Author keywords

Cryptography; Fibonacci numbers; Fractional order system; Synchronization

Indexed keywords

CHAOTIC BEHAVIORS; FEEDBACK CONTROLLER; FIBONACCI NUMBERS; FRACTIONAL ORDER; FRACTIONAL-ORDER CHAOTIC SYSTEMS; FRACTIONAL-ORDER SYSTEMS; ITS APPLICATIONS; STABILITY CONDITION;

EID: 84888605479     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-013-1032-3     Document Type: Article
Times cited : (98)

References (49)
  • 1
    • 0000241853 scopus 로고
    • Deterministic nonperiodic flow
    • 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
    • Lorenz, E.N.: Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130-141 (1963)
    • (1963) J. Atmos. Sci. , vol.20 , pp. 130-141
    • Lorenz, E.N.1
  • 3
    • 34547432043 scopus 로고    scopus 로고
    • Experimental confirmation of a new reversed butterfly-shaped attractor
    • 10.1088/1009-1963/16/7/015
    • Ling, L.; Yan-Chen, S.; Chong-Xin, L.: Experimental confirmation of a new reversed butterfly-shaped attractor. Chin. Phys. 16, 1897-1900 (2007)
    • (2007) Chin. Phys. , vol.16 , pp. 1897-1900
    • Ling, L.1    Yan-Chen, S.2    Chong-Xin, L.3
  • 4
    • 79953853477 scopus 로고    scopus 로고
    • Digital cryptography and feedback synchronization of chaotic systems
    • 10.1142/S0217979211057955
    • Mitra, M.; Banerjee, S.: Digital cryptography and feedback synchronization of chaotic systems. Int. J. Mod. Phys. B 25, 521-529 (2011)
    • (2011) Int. J. Mod. Phys. B , vol.25 , pp. 521-529
    • Mitra, M.1    Banerjee, S.2
  • 5
    • 84879784135 scopus 로고    scopus 로고
    • A new chaos synchronization scheme and its application to secure communications
    • doi: 10.1007/s11071-013-0824-9
    • Zhang, L.-f.; An, X.-l.; Zhang, J.-g.: A new chaos synchronization scheme and its application to secure communications. Nonlinear Dyn. doi: 10.1007/s11071-013-0824-9
    • Nonlinear Dyn.
    • Zhang, L.-F.1    An, X.-L.2    Zhang, J.-G.3
  • 6
    • 34347330038 scopus 로고    scopus 로고
    • A necessary condition for double scroll attractor existence in fractional-order systems
    • 10.1016/j.physleta.2007.05.081
    • Travazoei, M.S.; Haeri, M.: A necessary condition for double scroll attractor existence in fractional-order systems. Phys. Lett. A 367, 102-113 (2007)
    • (2007) Phys. Lett. A , vol.367 , pp. 102-113
    • Travazoei, M.S.1    Haeri, M.2
  • 8
    • 0346910376 scopus 로고    scopus 로고
    • New 3D-scroll attractors in hyperchaotic Chua's circuits forming a ring
    • 2020987 10.1142/S0218127403008284
    • Cafagna, D.; Grassi, G.: New 3D-scroll attractors in hyperchaotic Chua's circuits forming a ring. Int. J. Bifurc. Chaos Appl. Sci. Eng. 13, 2889-2903 (2003)
    • (2003) Int. J. Bifurc. Chaos Appl. Sci. Eng. , vol.13 , pp. 2889-2903
    • Cafagna, D.1    Grassi, G.2
  • 9
    • 10944251999 scopus 로고    scopus 로고
    • Design and analysis of multiscroll chaotic attractors from saturated function series
    • 10.1109/TCSI.2004.838151
    • Lü, J.; Chen, G.; Yu, X.; Leung, H.: Design and analysis of multiscroll chaotic attractors from saturated function series. IEEE Trans. Circuits Syst. I 51, 2476-2490 (2004)
    • (2004) IEEE Trans. Circuits Syst. i , vol.51 , pp. 2476-2490
    • Lü, J.1    Chen, G.2    Yu, X.3    Leung, H.4
  • 11
    • 0041384356 scopus 로고    scopus 로고
    • Chaotic dynamics of the fractional Lorenz system
    • 034101 10.1103/PhysRevLett.91.034101
    • Grigorenko, I.; Grigorenko, E.: Chaotic dynamics of the fractional Lorenz system. Phys. Rev. Lett. 91, 034101 (2003)
    • (2003) Phys. Rev. Lett. , vol.91
    • Grigorenko, I.1    Grigorenko, E.2
  • 12
    • 41849104190 scopus 로고    scopus 로고
    • A note on the fractional-order Chua's system
    • 10.1016/j.chaos.2006.10.054
    • Petras, I.: A note on the fractional-order Chua's system. Chaos Solitons Fractals 38, 140-147 (2008)
    • (2008) Chaos Solitons Fractals , vol.38 , pp. 140-147
    • Petras, I.1
  • 13
    • 2042470796 scopus 로고    scopus 로고
    • Chaos in the fractional order Chen system and its control
    • 10.1016/j.chaos.2004.02.035
    • Li, C.; Chen, G.: Chaos in the fractional order Chen system and its control. Chaos Solitons Fractals 22, 549-554 (2004)
    • (2004) Chaos Solitons Fractals , vol.22 , pp. 549-554
    • Li, C.1    Chen, G.2
  • 14
    • 23144435914 scopus 로고    scopus 로고
    • A note on the fractional-order Chen system
    • 10.1016/j.chaos.2005.04.037
    • Lu, J.G.; Chen, G.: A note on the fractional-order Chen system. Chaos Solitons Fractals 27, 685-688 (2006)
    • (2006) Chaos Solitons Fractals , vol.27 , pp. 685-688
    • Lu, J.G.1    Chen, G.2
  • 15
    • 18844427587 scopus 로고    scopus 로고
    • Chaos synchronization of the fractional Lü system
    • 10.1016/j.physa.2005.01.021
    • Deng, W.H.; Li, C.P.: Chaos synchronization of the fractional Lü system. Physica A 353, 61-72 (2005)
    • (2005) Physica A , vol.353 , pp. 61-72
    • Deng, W.H.1    Li, C.P.2
  • 16
    • 67649861441 scopus 로고    scopus 로고
    • Dynamic analysis of a fractional-order Lorenz chaotic system
    • 2554825 10.1016/j.chaos.2009.03.016
    • Yu, Y.; Li, H.X.; Wang, S.; Yu, J.: Dynamic analysis of a fractional-order Lorenz chaotic system. Chaos Solitons Fractals 42, 1181-1189 (2009)
    • (2009) Chaos Solitons Fractals , vol.42 , pp. 1181-1189
    • Yu, Y.1    Li, H.X.2    Wang, S.3    Yu, J.4
  • 18
    • 33845466254 scopus 로고    scopus 로고
    • Chaotic dy-namics of the fractionally damped Duffing equation
    • 10.1016/j.chaos.2005.11.066
    • Sheu, L.J.; Chen, H.K.; Chen, J.H.; Tam, L.M.: Chaotic dy-namics of the fractionally damped Duffing equation. Chaos Solitons Fractals 31, 1459-1468 (2007)
    • (2007) Chaos Solitons Fractals , vol.31 , pp. 1459-1468
    • Sheu, L.J.1    Chen, H.K.2    Chen, J.H.3    Tam, L.M.4
  • 19
    • 34147144036 scopus 로고    scopus 로고
    • Chaos in a fractional order modi-fied Duffing system
    • 10.1016/j.chaos.2005.11.059
    • Ge, Z.M.; Ou, C.Y.: Chaos in a fractional order modi-fied Duffing system. Chaos Solitons Fractals 34, 262-291 (2007)
    • (2007) Chaos Solitons Fractals , vol.34 , pp. 262-291
    • Ge, Z.M.1    Ou, C.Y.2
  • 21
    • 34548530905 scopus 로고    scopus 로고
    • Chaotic dynamics of the fractionally damped van der Pol equation
    • 10.1016/j.chaos.2006.05.010
    • Chen, J.H.; Chen, W.C.: Chaotic dynamics of the fractionally damped van der Pol equation. Chaos Solitons Fractals 35, 188-198 (2008)
    • (2008) Chaos Solitons Fractals , vol.35 , pp. 188-198
    • Chen, J.H.1    Chen, W.C.2
  • 22
    • 33846377845 scopus 로고    scopus 로고
    • Chaos in a modified van der Pol system and in its fractional order systems
    • 10.1016/j.chaos.2005.12.024
    • Ge, Z.M.; Zhang, A.R.: Chaos in a modified van der Pol system and in its fractional order systems. Chaos Solitons Fractals 32, 1791-1822 (2007)
    • (2007) Chaos Solitons Fractals , vol.32 , pp. 1791-1822
    • Ge, Z.M.1    Zhang, A.R.2
  • 25
    • 67449143115 scopus 로고    scopus 로고
    • Generalized projective synchronization of the fractional-order Chen hyperchaotic system
    • 10.1007/s11071-008-9416-5
    • Wu, X.; Lu, Y.: Generalized projective synchronization of the fractional-order Chen hyperchaotic system. Nonlinear Dyn. 57, 25-35 (2009)
    • (2009) Nonlinear Dyn. , vol.57 , pp. 25-35
    • Wu, X.1    Lu, Y.2
  • 26
    • 78049454811 scopus 로고    scopus 로고
    • Chaos and hybrid projective synchronization of commensurate and incommensurate fractional-order Chen-Lee systems
    • 10.1007/s11071-010-9767-6
    • Ching-Ming, C.; Hsien-Keng, C.: Chaos and hybrid projective synchronization of commensurate and incommensurate fractional-order Chen-Lee systems. Nonlinear Dyn. 62, 851-858 (2010)
    • (2010) Nonlinear Dyn. , vol.62 , pp. 851-858
    • Ching-Ming, C.1    Hsien-Keng, C.2
  • 27
    • 84867977717 scopus 로고    scopus 로고
    • Chaos in the fractional-order complex Lorenz system and its synchronization
    • 3010577 10.1007/s11071-012-0656-z
    • Luo, C.; Wang, X.: Chaos in the fractional-order complex Lorenz system and its synchronization. Nonlinear Dyn. 71, 241-257 (2013)
    • (2013) Nonlinear Dyn. , vol.71 , pp. 241-257
    • Luo, C.1    Wang, X.2
  • 28
    • 33847065079 scopus 로고    scopus 로고
    • Synchronization of fractional order chaotic systems
    • 2287821 10.1016/j.physleta.2006.11.053
    • Peng, G.: Synchronization of fractional order chaotic systems. Phys. Lett. A 363, 426-432 (2007)
    • (2007) Phys. Lett. A , vol.363 , pp. 426-432
    • Peng, G.1
  • 29
    • 33749553588 scopus 로고    scopus 로고
    • The synchronization of three fractional differential systems
    • 2280115 10.1016/j.chaos.2005.11.020
    • Li, C.; Yan, J.: The synchronization of three fractional differential systems. Chaos Solitons Fractals 32, 751-757 (2007)
    • (2007) Chaos Solitons Fractals , vol.32 , pp. 751-757
    • Li, C.1    Yan, J.2
  • 30
    • 27744554781 scopus 로고    scopus 로고
    • Chaos synchronization of the Chua system with a fractional order
    • 2186261 10.1016/j.physa.2005.06.078
    • Li, C.P.; Deng, W.H.; Xu, D.: Chaos synchronization of the Chua system with a fractional order. Physica A 360, 171-185 (2006)
    • (2006) Physica A , vol.360 , pp. 171-185
    • Li, C.P.1    Deng, W.H.2    Xu, D.3
  • 31
    • 41849090145 scopus 로고    scopus 로고
    • Chaos in the fractional order unified system and its synchronization
    • 10.1016/j.jfranklin.2007.11.003
    • Wu, X.; Li, J.; Chen, G.J.: Chaos in the fractional order unified system and its synchronization. J. Franklin Inst. 345, 392-401 (2008)
    • (2008) J. Franklin Inst. , vol.345 , pp. 392-401
    • Wu, X.1    Li, J.2    Chen, G.J.3
  • 32
    • 84863986004 scopus 로고    scopus 로고
    • Synchronization of nonidentical chaotic fractional-order systems with different orders of fractional derivatives
    • 2943362 10.1007/s11071-011-0322-x
    • Wang, Z.; Huang, X.; Zhao, Z.: Synchronization of nonidentical chaotic fractional-order systems with different orders of fractional derivatives. Nonlinear Dyn. 69, 999-1007 (2012)
    • (2012) Nonlinear Dyn. , vol.69 , pp. 999-1007
    • Wang, Z.1    Huang, X.2    Zhao, Z.3
  • 33
    • 79953836327 scopus 로고    scopus 로고
    • Chaos synchronization of fractional order unified chaotic system via nonlinear control
    • 10.1142/S0217979211058018
    • Chen, X.R.; Liu, C.X.: Chaos synchronization of fractional order unified chaotic system via nonlinear control. Int. J. Mod. Phys. B 25, 407-415 (2011)
    • (2011) Int. J. Mod. Phys. B , vol.25 , pp. 407-415
    • Chen, X.R.1    Liu, C.X.2
  • 34
    • 84863988396 scopus 로고    scopus 로고
    • Adaptive synchronization of the energy resource systems with mismatched parameters via linear feedback control
    • 10.1007/s11071-011-0321-y
    • Shi, X.; Wang, Z.: Adaptive synchronization of the energy resource systems with mismatched parameters via linear feedback control. Nonlinear Dyn. 69, 993-997 (2012)
    • (2012) Nonlinear Dyn. , vol.69 , pp. 993-997
    • Shi, X.1    Wang, Z.2
  • 35
    • 84866101967 scopus 로고    scopus 로고
    • Synchronization between fractional-order Ravinovich-Fabrikant and Lotka-Volterra systems
    • 2945558 10.1007/s11071-012-0426-y
    • Agrawal, S.K.; Srivastava, M.; Das, S.: Synchronization between fractional-order Ravinovich-Fabrikant and Lotka-Volterra systems. Nonlinear Dyn. 69, 2277-2288 (2012)
    • (2012) Nonlinear Dyn. , vol.69 , pp. 2277-2288
    • Agrawal, S.K.1    Srivastava, M.2    Das, S.3
  • 36
    • 84867897789 scopus 로고    scopus 로고
    • Studying on the stability of fractional-order nonlinear system
    • 2991287 10.1007/s11071-012-0469-0
    • Zhao, L.-D.; Hu, J.-B.; Fang, J.-A.; Zhang, W.-B.: Studying on the stability of fractional-order nonlinear system. Nonlinear Dyn. 70, 475-479 (2012)
    • (2012) Nonlinear Dyn. , vol.70 , pp. 475-479
    • Zhao, L.-D.1    Hu, J.-B.2    Fang, J.-A.3    Zhang, W.-B.4
  • 37
    • 84874203806 scopus 로고    scopus 로고
    • The synchronization of a fractional-order chaotic system
    • Zhang, f.-d.: The synchronization of a fractional-order chaotic system. Adv. Mater. Res. 655-657, 1488-1491 (2013)
    • (2013) Adv. Mater. Res. , vol.655-657 , pp. 1488-1491
    • Zhang, F.-D.1
  • 38
    • 84876135497 scopus 로고    scopus 로고
    • Adaptive control and synchronization of a fractional-order chaotic system
    • 10.1007/s12043-012-0500-5
    • Li, C.; Tong, Y.: Adaptive control and synchronization of a fractional-order chaotic system. PRAMANA J. Phys. 80, 583-592 (2013)
    • (2013) PRAMANA J. Phys. , vol.80 , pp. 583-592
    • Li, C.1    Tong, Y.2
  • 39
    • 84867882409 scopus 로고    scopus 로고
    • Analysis and synchronization for a new fractional-order chaotic system with absolute value term
    • doi: 10.1007/s11071-012-0480-5
    • Huang, L.; Liu, A.: Analysis and synchronization for a new fractional-order chaotic system with absolute value term. Nonlinear Dyn. doi: 10.1007/s11071-012-0480-5
    • Nonlinear Dyn.
    • Huang, L.1    Liu, A.2
  • 40
    • 84859845956 scopus 로고    scopus 로고
    • Generalized synchronization and control for incommensurate fractional unified chaotic system and applications in secure communication
    • 2954320
    • Liang, H.; Wang, Z.; Yue, Z.; Lu, R.: Generalized synchronization and control for incommensurate fractional unified chaotic system and applications in secure communication. Kybernetika 48, 190-205 (2012)
    • (2012) Kybernetika , vol.48 , pp. 190-205
    • Liang, H.1    Wang, Z.2    Yue, Z.3    Lu, R.4
  • 41
    • 84873400331 scopus 로고    scopus 로고
    • A new image encryption algorithm based on the fractional-order hyperchaotic Lorenz system
    • 010504 10.1088/1674-1056/22/1/010504
    • Zhen, W.; Xia, H.; Yu-Xia, Li.; Xiao-Na, S.: A new image encryption algorithm based on the fractional-order hyperchaotic Lorenz system. Chin. Phys. B. 22, 010504 (2013)
    • (2013) Chin. Phys. B. , vol.22
    • Zhen, W.1    Xia, H.2    Yu-Xia, Li.3    Xiao-Na, S.4
  • 42
    • 33750295344 scopus 로고    scopus 로고
    • Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models
    • 2273544 10.1016/j.jmaa.2006.01.087
    • Ahmed, E.; El-sayed, A.M.A.; El-Saka, H.A.A.: Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models. J. Math. Anal. Appl. 325, 542-553 (2007)
    • (2007) J. Math. Anal. Appl. , vol.325 , pp. 542-553
    • Ahmed, E.1    El-Sayed, A.M.A.2    El-Saka, H.A.A.3
  • 44
    • 0041622971 scopus 로고
    • Statistical geometry of a Cantor diocretum and semiconductors
    • 10.1016/0898-1221(95)00062-4
    • Naschie, M.S.El: Statistical geometry of a Cantor diocretum and semiconductors. Comput. Math. Appl. 29, 103-110 (1995)
    • (1995) Comput. Math. Appl. , vol.29 , pp. 103-110
    • Naschie, M.S.E.1
  • 46
    • 0009380542 scopus 로고
    • A history of the Fibonacci Q-matrix and a higher-dimensional problem
    • Gould, H.W.: A history of the Fibonacci Q-matrix and a higher-dimensional problem. Fibonacci Q. 19, 250-257 (1981)
    • (1981) Fibonacci Q. , vol.19 , pp. 250-257
    • Gould, H.W.1
  • 47
    • 26844477045 scopus 로고
    • Fibonacci properties by matrix methods
    • 10.2307/3617892
    • Silvester, J.R.: Fibonacci properties by matrix methods. Math. Gaz. 63, 188-191 (1979)
    • (1979) Math. Gaz. , vol.63 , pp. 188-191
    • Silvester, J.R.1
  • 48
    • 18544379418 scopus 로고    scopus 로고
    • A generalization of the Fibonacci Q-matrix
    • 1737613
    • Stakhov, O.P.: A generalization of the Fibonacci Q-matrix. Rep. Natl. Acad. Sci. 9, 46-49 (1999)
    • (1999) Rep. Natl. Acad. Sci. , vol.9 , pp. 46-49
    • Stakhov, O.P.1


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