Synchronization and estimation of jump parameter of one certain chaotic circuit

Abstract

Abstract:

Based on the Lyapunov stability and matrix theory, two schemes are used to estimate the unknwon jump parameters of one certain chaotic circuit and complete synchronization is realized . Theoretical analysis is given and checked by the numerical simulation. Within the first scheme, some unknown jump parameters(parameters jump suddenly) are identified completely by stabilizing the chaotic system to stable state and the critical value for negative feedback coefficient could be found by calculating the conditional Lyapunov exponents of the controlled system.Within the second scheme, parameter observers and controllers with controllable gain coefficient are approached theoretically by using the Lyapunov stability theory. Five unknown parameters are estimated exactly within short transient period when the two chaotic circuits reach complete synchronization. Finally, the two schemes are compared and discussed in brief.

Key words: quantum optics, chaos, parameter estimation, synchronization

CHU Run-Tong, WANG Chun-Ni, MA Jun. Synchronization and estimation of jump parameter of one certain chaotic circuit[J]. J4, 2010, 27(1): 82-87.

References

[1] Boccaletti S, Kurths J, Osipov G, et al. The synchronization of chaotic systems
[J]. Physics Reports.2002, 366: 1-101.

[2] Boccaletti S, Grebogi C, Lai Y C, et al. The control of chaos: Theroy and Applications
[J].Physics Reports, 2000, 329:103-197.

[3]Ma Jun, Wang Qingyun, Jin Wuyin et al. Control chaos in the Hindmarsh-Rose neuron by using intermittent feedback with one variable
[J]. Chinese. Physics Letters, 2008, 25(10):3582-3585.

[4]Wei Duqu, Luo Xiaoshu. Passive adaptive control of chaos in synchronous reluctance motor
[J]. Chinese Physics, 2008, 17(1): 92-97.

[5]Ma Jun, Pu Zhongsheng, Tang Guoning. Control L.C Oscillator Hyperchaotic System to Reach Arbitrary Desired Target
[J]. Chinese Journal of Simulation, 2004,16(6):1336-1339.

[6]Wang Haixia, Lu Qishao, Wang Qingyun. Complete Synchronization in Coupled Chaotic HR Neurons with Symmetric Coupling schemes
[J]. Chinese .Physics Letters, 2005, 22(9): 2173-2175.

[7]Xiao Yuzhu, Xu Wei. Complete synchronization between two bi-directionally coupled chaotic systems via an adaptive feedback controller
[J]. Chinese Physics, 2007, 16(6): 1597-1602.

[8]Yang Junzhong, Zhang Mei. Generalized Synchronization in a Drive-Response System
[J]. Communications in Theoretical Physics, 2008, 49(2): 391-395.

[9]Shuai Jianwei, Durand D M. Phase synchronization in two coupled chaotic neurons
[J]. Phys. Lett. A 1999, 264(4): 289-297.

[10]Vincent U E, Njah A N, Solarin A R T. Phase synchronization in bi-directionally coupled chaotic ratchets
[J]. Physica A ,2006, 360 (2): 186.

[11]Li Xiaowen, Zheng Zhigang. Phase Synchronization of Coupled Rössler Oscillators: Amplitude Effect
[J]. Communications in Theoretical Physics, 2007, 47(2): 265-269.

[12]Li Chuandong, Liao Xiaofeng. Lag synchronization of Rössler system and Chua circuit via a scalar signal
[J].Phys. Lett. A, 2004, 329 (4-5): 301-308.

[13]Li Guohui. Inverse lag synchronization of chaotic systems
[J]. Chinese Journal of Quantum Electronics,2008,25(4):467-470

[14]Zhang Chaoxia, Yu Simin. A scheme for hyperchaotic secure communication and its implementation via digital signal processor
[J]. Chinese Journal of Quantum Electronics,2009, 26(4) 456-464 .

[15]Wu Danhui, Li Qianghua, Song Lingfang. Application research on the chaos synchronization self-maintenance characteristic to secret communication
[J]. Chinese Journal of Quantum Electronics,2006, 23(4):511-515.

[16] Mu Jing, Tao Chao, Du Gonghua. Synchronization of the time-varying parameter chaotic system and its application to secure communication
[J].Chinese Physics, 2003, 12(4): 381-388.

[17]Wu Liang and Zhu Shiqun. Communications using multi-mode laser system based on chaotic synchronization
[J]. Chinese Physics, 2003, 12(3): 300-304.

[18]Ma Jun, Wang Chunni, Wei Zhiqiang, Pu Zhongsheng. Synchronization and parameter identification of Rössler Hyperchaotic System
[J]. Chinese Journal of Simulation, 2005,17(12): 3028-3032.

[19]Elabbasy E M and El-Dessoky M M. Adaptive synchronization for four-scroll attractor with fully unknown parameters
[J]. Phys. Lett. A ,2006, 349(1-4) 187-191.

[20]Gao Bingjian and Lu Jun’an. Adaptive synchronization of hyperchaotic Lü system with uncertainty
[J]. Chinese Physics, 2007, 16(3): 666-670.

[21]Ren Haipeng, Yin Jia, Zheng Gang, Han Chongzhao. On parameter identification methods of chaotic system based on adaptive synchronization
[J]. Chinese Journal of Quantum Electronics,2009, 26(4) 456-464 .

[22] Pikovsky A S, Rabinovich M I. A simple autogenerator with stochastic behavior
[J]. Dokl. Akad. Nauk SSSR, 1978, 239:301-304.