Adaptive Generalized Combination Complex Synchronization and Parameter Identification of Hyperchaotic Complex Systems
WANG Shibing①② WANG Xingyuan①
①(Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024, China) ②(School of Computer and Information Engineering, Fuyang Normal University, Fuyang 236041, China)
Based on adaptive control and Lyapunov stability theory, a novel adaptive Generalized Combination Complex Synchronization (GCCS) scheme is proposed for nonidentical hyperchaotic complex systems with unknown parameters. Firstly, the definition of GCCS is presented, and synchronization of drive-response systems is transformed to the zero solution analysis of the error dynamical system. Secondly, a nonlinear feedback controller and parameter update laws are theoretically designed, wherein error feedback gains are introduced to control synchronization speed. Finally, GCCS among the hyperchaotic complex Lorenz system, complex Chen system, and complex Lü system is carried out to verify the correctness and effectiveness of the proposed scheme by numerical simulation.
PECORA L M and CARROLL T L. Synchronization in chaotic systems [J]. Physical Review Letters, 1990, 64(8): 821-824. doi: 10.1103/PhysRevLett.64.821.
[2]
SUN Zhiyong, SI Gangquan, MIN Fuhong, et al. Adaptive modified function projective synchronization and parameter identification of uncertain hyperchaotic (chaotic) systems with identical or non-identical structures[J]. Nonlinear Dynamics, 2012, 68(4): 471-486. doi: 10.1007/s11071-011-0230-0.
[3]
ZHANG Fangfang. Lag synchronization of complex Lorenz system with applications to communication[J]. Entropy, 2015, 17(7): 4974-4985. doi: 10.3390/e17074974.
YU Simin, LÜ Jinhu, and LI Chengqing. Some progresses of chaotic cipher and its applications in multimedia secure communications[J]. Journal of Electronics & Information Technology, 2016, 38(3): 735-752. doi: 10.11999/JEIT151356.
ZHANG Youan, YU Mingzhe, and GENG Baoliang. Adaptive synchronization of uncertain fractional-order chaotic systems based on projective method[J]. Journal of Electronics & Information Technology, 2015, 37(2): 455-460. doi: 10.11999/ JEIT140514.
[7]
MAHMOUD G M, BOUNTIS T, ABDEL-LATIF G M, et al. Chaos synchronization of two different chaotic complex Chen and Lü systems[J]. Nonlinear Dynamics, 2008, 55(1): 43-53. doi: 10.1007/s11071-008-9343-5.
[8]
ZHOU Xiaobing, XIONG Lianglin, CAI Weiwei, et al. Adaptive synchronization and antisynchronization of a hyperchaotic complex Chen system with unknown parameters based on passive control[J]. Journal of Applied Mathematics, 2013, 23(1): 309-338. doi: 10.1155/2013/845253.
[9]
WANG Xingyuan and ZHANG Hao. Backstepping-based lag synchronization of a complex permanent magnet synchronous motor system[J]. Chinese Physics B, 2013, 22(4): 558-562. doi: 10.1088/1674-1056/22/4/048902.
[10]
MAHMOUD G M and MAHMOUD E E. Phase and antiphase synchronization of two identical hyperchaotic complex nonlinear systems[J]. Nonlinear Dynamics, 2010, 61(1-2): 141-152. doi: 10.1007/s11071-009-9637-2.
[11]
WANG Shibing, WANG Xingyuan, and ZHOU Yufei. A memristor-based complex Lorenz system and its modified projective synchronization[J]. Entropy, 2015, 17(11): 7628-7644. doi: 10.3390/e17117628.
[12]
LIU Jian, LIU Shutang, and YUAN Chunhua. Adaptive complex modified projective synchronization of complex chaotic (hyperchaotic) systems with uncertain complex parameters[J]. Nonlinear Dynamics, 2015, 79(2): 1035-1047. doi: 10.1007/s11071-014-1721-6.
[13]
WANG Shibing, WANG Xingyuan, and HAN Bo. Complex generalized synchronization and parameter identification of nonidentical nonlinear complex systems[J]. PLoS One, 2016, 11(3): e0152099. doi: 10.1371/journal.Pone.0152099.
[14]
ZHOU Xiaobing, JIANG Murong, and HUANG Yaqun. Combination synchronization of three identical or different nonlinear complex hyperchaotic systems[J]. Entropy, 2013, 15(9): 3746-3761. doi: 10.3390/e15093746.
[15]
SUN Junwei, CUI, Guangzhao, WANG Yanfeng, et al. Combination complex synchronization of three chaotic complex systems[J]. Nonlinear Dynamics, 2015, 79(2): 953-965. doi: 10.1007/s11071-014-1714-5.
[16]
JIANG Cuimei, LIU Shutang, and WANG Da. Generalized combination complex synchronization for fractional-order chaotic complex systems[J]. Entropy, 2015, 17(8): 5199-5217. doi: 10.3390/e17085199.
[17]
LUO Runzi, WANG Yinglan, and DENG Shucheng. Combination synchronization of three classic chaotic systems using active backstepping design[J]. Chaos, 2011, 21(4): 043114. doi: 10.1063/1.3655366.
[18]
RULKOV N F, SUSHCHIK M M, TSIMRING L S, et al. Generalized synchronization of chaos in directionally coupled chaotic systems[J]. Physical Review E, 1995, 51(2): 980-994. doi: 10.1103/PhysRevE.51.980.
