An Analytical Study on the Synchronization of Murali–Lakshmanan–Chua Circuits
G. Sivaganesh**
Alagappa Chettiar College of Engineering and Technology, Karaikudi Tamilnadu-630 004, India
Abstract :An explicit analytical solution is presented for unidirectionally coupled two Murali–Lakshmanan–Chua circuits exhibiting chaos synchronization in their dynamics. The transition of the system from an unsynchronized state to a state of complete synchronization under the influence of the coupling parameter is observed through phase portraits obtained from the analytical solutions of the circuit equations characterizing the system.
出版日期: 2014-12-23
:
05.45.Gg
(Control of chaos, applications of chaos)
05.45.Xt
(Synchronization; coupled oscillators)
[1] Chua L O, Kocarev L, Eckert K and Itoh M 1992 Int. J. Bifurcation Chaos Appl. Sci. Eng. 2 705 [2] Chua L O, Kocarev L, Eckert K and Itoh M 1993 J. Circuits Syst. Comput. 3 93 [3] Murali K and Lakshmanan M 1993 Phys. Rev. E 48 R1624 [4] Murali K and Lakshmanan M 1994 Phys. Rev. E 49 4882 [5] Murali K and Lakshmanan M 1995 Int. J. Bifurcation Chaos Appl. Sci. Eng. 5 563 [6] Murali K and Lakshmanan M 1996 Chaos Nonlinear Oscillators: Controlling Synchronization (Singapore: World Scientific) chap 9 p 239 [7] Murali K and Lakshmanan M 1997 Int. J. Bifurcation Chaos Appl. Sci. Eng. 7 415 [8] Erjaee G H 2009 Chaos Solitons Fractals 39 1195 [9] Mahmoud G M and Mahmoud E E 2010 Nonlinear Dyn. 62 875 [10] Cafagna D and Grassi G 2012 Nonlinear Dyn. 68 117 [11] Mahmoud G M and Mahmoud E E 2012 Nonlinear Dyn. 67 1613 [12] Boccaletti 2002 Phys. Rep. 366 1 [13] Wang S, Yu Y G, Wang H and Rahmani A 2014 Chin. Phys. B 23 040502 [14] Murali K, Lakshmanan M and Leon O Chua 1994 IEEE Trans. Circuits Syst. 41 462 [15] Murali K, Lakshmanan M and Chua L O 1994 Int. J. Bifurcation Chaos Appl. Sci. Eng. 4 1511 [16] Murali K and Lakshmanan M 1995 Philos. Trans. A 353 33 [17] Lakshmanan M and Rajasekar S 2003 Nonlinear Dynamics: Integrability Chaos Patterns (Berlin: Springer) chap 6 p 173 [18] Thamilmaran K and Lakshmanan M 2002 Int. J. Bifurcation Chaos Appl. Sci. Eng. 12 783 [19] Thamilmaran K, Senthil Kumar D V, Lakshmanan M and Ishaq Ahamed A 2005 Int. J. Bifurcation Chaos Appl. Sci. Eng. 15 637 [20] Manimehan I, Thamilmaran K and Philominathan P 2009 Int. J. Bifurcation Chaos Appl. Sci. Eng. 19 2347 [21] Arulgnanam A, Thamilmaran K and Daniel M 2009 Chaos Solitons Fractals 42 2246
[1]
. [J]. 中国物理快报, 2015, 32(03): 38201-038201.
[2]
. [J]. 中国物理快报, 2014, 31(06): 60502-060502.
[3]
. [J]. 中国物理快报, 2013, 30(6): 60501-060501.
[4]
. [J]. Chin. Phys. Lett., 2013, 30(2): 20501-020501.
[5]
Salman Ahmad, YUE Bao-Zeng. Bifurcation and Stability Analysis of the Hamiltonian–Casimir Model of Liquid Sloshing [J]. 中国物理快报, 2012, 29(6): 60501-060501.
[6]
LI Jian-Ping,YU Lian-Chun,YU Mei-Chen,CHEN Yong**. Zero-Lag Synchronization in Spatiotemporal Chaotic Systems with Long Range Delay Couplings [J]. 中国物理快报, 2012, 29(5): 50501-050501.
[7]
LI Hai-Yan**;HU Yun-An
. Backstepping-Based Synchronization Control of Cross-Strict Feedback Hyper-Chaotic Systems [J]. 中国物理快报, 2011, 28(12): 120508-120508.
[8]
SHANG Hui-Lin**;WEN Yong-Peng
. Fractal Erosion of the Safe Basin in a Helmholtz Oscillator and Its Control by Linear Delayed Velocity Feedback [J]. 中国物理快报, 2011, 28(11): 110503-110503.
[9]
KADIR Abdurahman;WANG Xing-Yuan**;ZHAO Yu-Zhang
. Generalized Synchronization of Diverse Structure Chaotic Systems [J]. 中国物理快报, 2011, 28(9): 90503-090503.
[10]
WANG Xing-Yuan**;QIN Xue;XIE Yi-Xin
. Pseudo-Random Sequences Generated by a Class of One-Dimensional Smooth Map [J]. 中国物理快报, 2011, 28(8): 80501-080501.
[11]
WANG Xing-Yuan**;REN Xiao-Li
. Chaotic Synchronization of Two Electrical Coupled Neurons with Unknown Parameters Based on Adaptive Control [J]. 中国物理快报, 2011, 28(5): 50502-050502.
[12]
GUO Rong-Wei
. Simultaneous Synchronization and Anti-Synchronization of Two Identical New 4D Chaotic Systems [J]. 中国物理快报, 2011, 28(4): 40205-040205.
[13]
SHI Si-Hong;YUAN Yong;WANG Hui-Qi;LUO Mao-Kang**
. Weak Signal Frequency Detection Method Based on Generalized Duffing Oscillator [J]. 中国物理快报, 2011, 28(4): 40502-040502.
[14]
JIANG Nan**;CHEN Shi-Jian
. Chaos Control in Random Boolean Networks by Reducing Mean Damage Percolation Rate [J]. 中国物理快报, 2011, 28(4): 40504-040504.
[15]
ZHANG Ying-Qian;WANG Xing-Yuan**
. A Parameter Modulation Chaotic Secure Communication Scheme with Channel Noises [J]. 中国物理快报, 2011, 28(2): 20505-020505.