Finite Time Symplectic Synchronization between Two Different Chaotic Systems

In this paper, the finite-time symplectic synchronization
between two different chaotic systems is investigated. Based on the
finite-time stability theory, a simple adaptive feedback scheme is
proposed to realize finite-time symplectic synchronization for the
Lorenz and L¨u systems. Numerical examples are provided to show
the effectiveness of the proposed method.

Authors:

• Chunming Xu

Keywords:

• Chaotic systems
• symplectic synchronization
• finite-time synchronization
• adaptive controller.

References:

[1] L.M. Pecora, T.L. Carroll: ”Synchronization in chaotic systems”; Phys.
Rev. Lett.,Vol. 64(8), 1990, 821-824.
[2] L. Kacarev, U. Parlitz: ”General approach for chaotic synchronization,
with application to communication”; Phys. Rev. Lett., Vol. 74(25), 1996,
5028-5031.
[3] R.A. Ims, H.P. Andreassen: ”Spatial synchronization of vole population
dynamics by predatory birds”; Nature, Vol. 408(9), 2000, 194-196.
[4] Y.N. Li, L. Chen, Z.S. Cai, X.Z. Zhao: ”Experimental study of chaos
synchronization in the Belousov-Zhabotinsky chemical system”; Chaos
Solitons Fractals, Vol. 22(4), 2004, 767-771.
[5] M. Barahnoa; L. M. Pecora: ”Synchronization in small- world systems”;
Physical Review Letters, Vol. 89(5), 2002, 54101-54104.
[6] S. Bowonga; M. Kakmenib, R. Koinac: ”Chaos synchronization and
duration time of a class of uncertain systems”; Mathematics and
Computers in Simulation, Vol. 71(3), 2006, 212-228.
[7] M. Mossa Al-sawalha; M. S. M. Nooran: ”Adaptive anti-synchronization
of chaotic systems with fully unknown parameters”; Computers and
Mathematics with Applications, Vol. 59(10), 2010, 3234-3244.
[8] G. Rosenblum; S. Pikovsky; J. Kurths: ”Phase Synchronization of Chaotic
Oscillators”; Physical Review Letters, Vol. 76(11), 1996, 1804-1807.
[9] S. Taherion; Y.C. Lai.: ”Observability of lag synchronization of coupled
chaotic oscillators”; Physical Review E, Vol. (59)(6), 1999, 6247-6250.
[10] Z. Wang: ”Projective synchronization of hyperchaotic Lu system and
Liu system”; Nonlinear Dynamics, Vol. 59(3), 2010, 455-462.
[11] S.S. Yang; K. Duan: ”Generalized synchronization in chaotic systems”;
Chaos Solitons and Fractals, Vol. 9(9), 1998, 1703-1707.
[12] H. Chen; M. Sun: ”Generalized projective synchronization of the energy
resource system”; International Journal of Nonlinear Science, Vol. 2(2),
2006, 142-149.
[13] X. Wang; L. Tian, L. Yu: ”Linear feedback controlling and
synchronization of the Chen’s chaotic system”; International Journal of
Nonlinear Science, Vol. 2(1), 2006, 43-49.
[14] Z.M. Ge; C.H. Yang: ”Symplectic synchronization of different chaotic
systems”; Chaos, Solitons and Fractals, Vol. 40(5), 2009, 2532-2543.
[15] S. Li; Y.P. Tian: ”Finite time synchronization of chaotic systems”; Chaos
Solitons Fractals, Vol. 10(4), 2003, 859-867.
[16] D. Zhang, J. Mei, P. Miao: ”Global finite-time synchronization of
different dimensional chaotic systems”; Applied Mathematical Modelling,
Vol. 48 (4), 2017, 303-315.
[17] M.P. Aghababa; S. Khanmohammadi; G. Alizadeh: ”Finite-time
synchronization of two different chaotic systems with unknown
parameters via sliding mode technique”; Applied Mathematical
Modelling, Vol. 35(6),2011, 3080-3091.
[18] R.W. Guo; U.E. Vincent: ”Finite time stabilization of chaotic systems
via single input”; Physics Letters A, Vol. 375(2), 2010, 119-124.
[19] Y.Y. Hou; Z.L. Wan, T.L. Liao: ”Finite-time synchronization of switched
stochastic Rossler systems”; Nonlinear Dynamics, Vol. 70(1), 2012,
315-322.
[20] N. Lorenz.: ”Deterministic nonperiodic flow”; Journal of the
Atmospheric Sciences, Vol. 20(2), 1963, 130-141.
[21] Y.W. Wang; Z.H. Guan: ”Generalized synchronization of continuous
chaotic systems”; British Journal of Clinical Pharmacology, Vol. 30(3),
2006, 734-747.
[22] H. Wang; Z.Z. Han; Q.Y. Xie; W. Zhang: ”Finite-time chaos
synchronization of unified chaotic system with uncertain parameters”;
Communications in Nonlinear Science and Numerical Simulation, Vol.
14(5), 2009, 2239-2247.
[23] S.H. Yu; X.H. Yu; B. Shirinzadeh; Z.H. Man: ”Continuous finite-time
control for robotic manipulators with terminal sliding mode”; Automatica,
Vol. 41(11), 2005, 1957-1964.