{"title":"Finite Time Symplectic Synchronization between Two Different Chaotic Systems","authors":"Chunming Xu","volume":127,"journal":"International Journal of Computer and Information Engineering","pagesStart":926,"pagesEnd":930,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10008554","abstract":"In this paper, the finite-time symplectic synchronization
\r\nbetween two different chaotic systems is investigated. Based on the
\r\nfinite-time stability theory, a simple adaptive feedback scheme is
\r\nproposed to realize finite-time symplectic synchronization for the
\r\nLorenz and L¨u systems. Numerical examples are provided to show
\r\nthe effectiveness of the proposed method.","references":"[1] L.M. Pecora, T.L. Carroll: \u201dSynchronization in chaotic systems\u201d; Phys.\r\nRev. Lett.,Vol. 64(8), 1990, 821-824.\r\n[2] L. Kacarev, U. Parlitz: \u201dGeneral approach for chaotic synchronization,\r\nwith application to communication\u201d; Phys. Rev. Lett., Vol. 74(25), 1996,\r\n5028-5031.\r\n[3] R.A. Ims, H.P. Andreassen: \u201dSpatial synchronization of vole population\r\ndynamics by predatory birds\u201d; Nature, Vol. 408(9), 2000, 194-196.\r\n[4] Y.N. Li, L. Chen, Z.S. Cai, X.Z. Zhao: \u201dExperimental study of chaos\r\nsynchronization in the Belousov-Zhabotinsky chemical system\u201d; Chaos\r\nSolitons Fractals, Vol. 22(4), 2004, 767-771.\r\n[5] M. Barahnoa; L. M. Pecora: \u201dSynchronization in small- world systems\u201d;\r\nPhysical Review Letters, Vol. 89(5), 2002, 54101-54104.\r\n[6] S. Bowonga; M. Kakmenib, R. Koinac: \u201dChaos synchronization and\r\nduration time of a class of uncertain systems\u201d; Mathematics and\r\nComputers in Simulation, Vol. 71(3), 2006, 212-228.\r\n[7] M. Mossa Al-sawalha; M. S. M. Nooran: \u201dAdaptive anti-synchronization\r\nof chaotic systems with fully unknown parameters\u201d; Computers and\r\nMathematics with Applications, Vol. 59(10), 2010, 3234-3244.\r\n[8] G. Rosenblum; S. Pikovsky; J. Kurths: \u201dPhase Synchronization of Chaotic\r\nOscillators\u201d; Physical Review Letters, Vol. 76(11), 1996, 1804-1807.\r\n[9] S. Taherion; Y.C. Lai.: \u201dObservability of lag synchronization of coupled\r\nchaotic oscillators\u201d; Physical Review E, Vol. (59)(6), 1999, 6247-6250.\r\n[10] Z. Wang: \u201dProjective synchronization of hyperchaotic Lu system and\r\nLiu system\u201d; Nonlinear Dynamics, Vol. 59(3), 2010, 455-462.\r\n[11] S.S. Yang; K. Duan: \u201dGeneralized synchronization in chaotic systems\u201d;\r\nChaos Solitons and Fractals, Vol. 9(9), 1998, 1703-1707.\r\n[12] H. Chen; M. Sun: \u201dGeneralized projective synchronization of the energy\r\nresource system\u201d; International Journal of Nonlinear Science, Vol. 2(2),\r\n2006, 142-149.\r\n[13] X. Wang; L. Tian, L. Yu: \u201dLinear feedback controlling and\r\nsynchronization of the Chen\u2019s chaotic system\u201d; International Journal of\r\nNonlinear Science, Vol. 2(1), 2006, 43-49.\r\n[14] Z.M. Ge; C.H. Yang: \u201dSymplectic synchronization of different chaotic\r\nsystems\u201d; Chaos, Solitons and Fractals, Vol. 40(5), 2009, 2532-2543.\r\n[15] S. Li; Y.P. Tian: \u201dFinite time synchronization of chaotic systems\u201d; Chaos\r\nSolitons Fractals, Vol. 10(4), 2003, 859-867.\r\n[16] D. Zhang, J. Mei, P. Miao: \u201dGlobal finite-time synchronization of\r\ndifferent dimensional chaotic systems\u201d; Applied Mathematical Modelling,\r\nVol. 48 (4), 2017, 303-315.\r\n[17] M.P. Aghababa; S. Khanmohammadi; G. Alizadeh: \u201dFinite-time\r\nsynchronization of two different chaotic systems with unknown\r\nparameters via sliding mode technique\u201d; Applied Mathematical\r\nModelling, Vol. 35(6),2011, 3080-3091.\r\n[18] R.W. Guo; U.E. Vincent: \u201dFinite time stabilization of chaotic systems\r\nvia single input\u201d; Physics Letters A, Vol. 375(2), 2010, 119-124.\r\n[19] Y.Y. Hou; Z.L. Wan, T.L. Liao: \u201dFinite-time synchronization of switched\r\nstochastic Rossler systems\u201d; Nonlinear Dynamics, Vol. 70(1), 2012,\r\n315-322.\r\n[20] N. Lorenz.: \u201dDeterministic nonperiodic flow\u201d; Journal of the\r\nAtmospheric Sciences, Vol. 20(2), 1963, 130-141.\r\n[21] Y.W. Wang; Z.H. Guan: \u201dGeneralized synchronization of continuous\r\nchaotic systems\u201d; British Journal of Clinical Pharmacology, Vol. 30(3),\r\n2006, 734-747.\r\n[22] H. Wang; Z.Z. Han; Q.Y. Xie; W. Zhang: \u201dFinite-time chaos\r\nsynchronization of unified chaotic system with uncertain parameters\u201d;\r\nCommunications in Nonlinear Science and Numerical Simulation, Vol.\r\n14(5), 2009, 2239-2247.\r\n[23] S.H. Yu; X.H. Yu; B. Shirinzadeh; Z.H. Man: \u201dContinuous finite-time\r\ncontrol for robotic manipulators with terminal sliding mode\u201d; Automatica,\r\nVol. 41(11), 2005, 1957-1964.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 127, 2017"}