Linear coupling-induced synchronization between periodic Chua oscillators

Abstract

Abstract: The complete synchronization between two nonlinear Chua circuits due to linear coupling is investigated based on Lyauponov stability. It is confirmed that the linear controllers is effective by constructing the exponential Lyapunov function, and the reliability of this scheme is confirmed by the numerical results. The transient period for complete synchronization and averaged power consumption of controller are associated with the selection of coupling intensity.

Key words: chaos, exponential Lyapunov function, linear-coupling, complete synchronization, chaos

CLC Number:

HE Yujun， CHU Run-tong，LI Fan. Linear coupling-induced synchronization between periodic Chua oscillators[J]. J4, 2013, 30(5): 601-607.

References

[1] Kinzel W, Englert A, Kanter I. On chaos synchronization and secure communication
[J]. Phil Trans R Soc A, 2010, 368:379-389.
[2] Luo X H,Li H Q,Chen Q H.A new method of adaptive tracking control for chaotic system
[J]. Acta Physica Sinica(物理学报),2009,58(11):7532-7538. (In chinese)
[3] Xu B R. A digital secure communication scheme based on generalized synchronization of non-autonomous chaotic system
[J]. Chinese Journal of Quantum Electronics(量子电子学报), 2011, 28 (6): 710-714.
[4] Liu P Y, Zhao Q C, Yin H X. Performance analysis of two types of chaotic optical secure communication schemes
[J]. Chinese Journal of Quantum Electronics(量子电子学报)，2012, 29(4): 500-506
[5] Perc M, Marhl M. Resonance effects determine the frequency of bursting Ca2+ oscillations
[J]. Chem Phys Lett, 2003, 376:432-437.
[6] Jang P Q, Zhou Y L. Luo X S et al. Synchronization in unidirectionally coupled hyperchaotic oscillators with a single variable and its realization of circuit experimental simulations
[J]. Acta. Phys. Sin. (物理学报), 2002, 51(9):1937-1941. (In chinese)
[7] Min F H, Wang Z Q. Coupled synchronization of the unified chaotic system
[J]. Acta. Phys. Sin.(物理学报), 2005, 54(9): 4026-2030.(In chinese)
[8] Sun J, Pan T, Xu G D. Spatiotemporal chaos synchronization in two-dimensional lattice arrays of locally coupled lasers
[J]. Chinese Journal of Quantum Electronics(量子电子学报)，2009, 26(6): 708-714.
[9] Chu R T, Wang C N, Ma J. Synchronization and estimation of jump parameter of one certain circuit
[J]. Chinese Journal of Quantum Electronics(量子电子学报), 2010, 27(1): 82-87.
[10] Sun R S, Hua D Y. Synchronization of Local Oscillations in a Spatial Rock–Scissors–Paper Game Mode
[J]. Chin Phys Lett, 2009, 26(8):086403-3.
[11] Guan J B. Synchronization Control of Two Different Chaotic Systems with Known and unknown Parameters
[J]. Chin Phys Lett, 2010, 27(2):020502-4.
[12] Andrievsky B. Adaptive synchronization methods for signal transmission on chaotic carriers
[J]. Math Comput Simul, 2002, 58(4–6):285–293.
[13] Wang Q Y, Lu Q S, Wang H X. Transition to complete synchronization via nearly synchronization in two coupled chaotic neurons
[J]. Chin Phys, 2005, 14(11):2189–2195.
[14] Abdurahman K, Wang X Y, Zhao Y Z. Generalized Synchronization of Diverse Structure Chaotic Systems
[J]. Chin Phys Lett, 2011, 28(9):090503-4.
[15] Wang S, Yu Y G. Generalized Projective Synchronization of Fractional Order Chaotic Systems with different Dimensions
[J]. Chin Phys Lett, 2012, 29(2):020505-3.
[16] Wang J A, Liu H P. Adaptive Synchronization of an Array of Time-Varying Coupled Delayed Neural Networks
[J]. Chin Phys Lett, 2010, 27(3):030505-4.
[17] Zheng Y A. Adaptive Generalized Projective Synchronization of Takagi-Sugeno Fuzzy Drive-response Dynamical Networks with Time Delay
[J]. Chin Phys Lett, 2012, 29(2):020502-4
[18] Du Y, Sun W G, Li P C. Adaptive synchronization between two nonlinear coupled networks
[J]. Comm. On appl. Math .and compt.(应用数学与计算机学报), 2009, 23(2):87-94
[19] Liu B J, Cai L, Feng C W. Adaptive generalized synchronization of simple piecewise linear chaotic system and SETMOS chaotic system
[J]. Chinese Journal of Quantum Electronics(量子电子学报), 2012, 29(1):74-79
[20] Zhang Y, Lu S, Wang Y H. Synchronization of Chaos in Time-Delayed Systems under Parameter Mismatch
[J]. Chin Phys Lett, 2009, 26(9):090501-4.
[21] Yu H J, Peng J H. Synchronization of nonlinear coupled hyper-chaotic R?ssler systems and networks
[J]. Chinese Journal of Computational Physics(计算物理), 2006, 23(5):626-630
[22] Cang S J, Chen Z Q, Yuan Z Z. Analysis and circuit implementation of a new four-dimensional non-autonomous hyper-chaotic system
[J]. Acta. Phys. Sin. (物理学报), 2008,57(03): 1493-1501.(In Chinese )
[23] Li F, Liu Q R, Guo H Y. Simulating the electric activity of FitzHugh–Nagumo neuron by using Josephson junction model
[J]. Nolinear Dynamics, 2012, 69:2169?2179.
[24] Luo Y J, Yu Q, Zhang W D. Research on impulsive synchronization approach of parameter uncertain hyperchaotic systems with time-delay
[J]. Acta. Phys. Sin. (物理学报), 2011, 60(11): 110504-8.(In chinese)
[25] Jia L X, Dai H, Hui M. A new four-dimensional hyperchaotic Chen system and its generalized synchronization
[J]. Chin Phys B, 2010, 19(10):100501.
[26] Rosenblum M G, Pikovsky A S，J Kurths. Phase synchronization of chaotic Oscillators
[J]. Physical Review Letters, 1996, 76:1804-1807.
[27] Sarasola C, Torrealdea F J, d’Anjou A et al. Cost of Synchronizing Different Chaos Systems
[J].Math Comput Simula, 2002, 58: 309–327.
[28] Perc M. Effects of small-world connectivity on noise-induced temporal spatial order in neural media
[J]. Chaos Solitons and Fractals, 2007, 31:280–291.