-
Previous Article
Joint backoff control in time and frequency for multichannel wireless systems and its Markov model for analysis
- DCDS-B Home
- This Issue
-
Next Article
Feature extraction of the patterned textile with deformations via optimal control theory
Synchronization of chaotic systems with time-varying coupling delays
1. | Texas A&M University at Qatar, Doha, P.O.Box 23874, Qatar |
2. | Department of Electronic Engineering, City University of Hong Kong, Hong Kong, China |
3. | Institute for Physics, University of Potsdam, Am Neuen Palais, Gebude 19, D-14415 Potsdam, Germany |
References:
[1] |
S. Boccaletti, J. Kurths, G. Osipov, D. L. Vallares and C. S. Zhou, The synchronization of chaotic systems, Phys. Rep., 366 (2002), 1-101.
doi: 10.1016/S0370-1573(02)00137-0. |
[2] |
S. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan, "Linear Matrix Inequalities In Systems And Control Theory," SIAM Studies in Applied Mathematics, 15, SIAM, Philadephia, PA, 1994. |
[3] |
J. Cao and J. Lu, Adaptive synchronization of neural networks with or without time-varying delay, Chaos, 16 (2006), 013133, 6 pp. |
[4] |
P. Colet and R. Roy, Digital communication with synchronized chaotic lasers, Opt. Lett., 19 (1994), 2056.
doi: 10.1364/OL.19.002056. |
[5] |
K. Gopalsamy, "Stability and Oscillations in Delay Differential Equations of Population Dynamics," Mathematics and its Applications, 74, Kluwer Academic Publishers Group, Dordrecht, 1992. |
[6] |
H. G. Schuster, ed., "Handbook of Chaos Control: Foundations and Applications," Wiley-VCH, Weinheim, 1999. |
[7] |
H. Huang, G. Feng and Y. Sun, Robust synchronization of chaotic systems subject to parameter uncertainties, Chaos, 19 (2009), 033128.
doi: 10.1063/1.3212940. |
[8] |
T. Huang, C. Li and X. Liu, Synchronization of chaotic systems with delay using intermittent linear state feedback, Chaos, 18 (2008), 033122, 8 pp. |
[9] |
C. Li, G. Feng and X. Liao, Stabilization of nonlinear systems via periodically intermittent control, IEEE Trans. Circuits and Systems II, 54 (2006), 1019-1023. |
[10] |
C. Li, X. Liao and K. Wong, Chaotic lag synchronization of coupled time-delayed systems and its application in secure communication, Physica D, 194 (2004), 187-202.
doi: 10.1016/j.physd.2004.02.005. |
[11] |
X. Liu, T. Chen and W. Lu, Cluster synchronization for linearly coupled complex networks, Journal of Industrial and Management Optimization (JIMO), 7 (2011), 87-101.
doi: 10.3934/jimo.2011.7.87. |
[12] |
J. Lu, J. Cao and D. Ho, Adaptive stabilization and synchronization for chaotic lur’e systems with time-varying delay, IEEE Transactions on Circuits and Systems I: Regular Papers, 55 (2008), 1347-1356.
doi: 10.1109/TCSI.2008.916462. |
[13] |
L. M. Pecora and T. L. Carroll, Synchronization in chaotic systems, Phys. Rev. Lett., 64 (1990), 821-824.
doi: 10.1103/PhysRevLett.64.821. |
[14] |
J. Qing, Projective synchronization of a new hyperchaotic Lorenz system, Physics Letters A, 370 (2007), 40-45.
doi: 10.1016/j.physleta.2007.05.028. |
[15] |
F. Rogister, D. Pieroux, M. Sciamanna, P. Megret and M. Blondel, Anticipating synchronization of two chaotic laser diodes by incoherent optical coupling and its application to secure communications, Optics Communications, 207 (2002), 295-306.
doi: 10.1016/S0030-4018(02)01494-3. |
[16] |
M. Rosenblum and A. Pikovsky, Phase synchronization of chaotic oscillators, Phys. Rev. Lett., 76 (1996), 1804-1807.
doi: 10.1103/PhysRevLett.76.1804. |
[17] |
N. Rulkov and M. Sushchik, Generalized synchronization of chaos in directionally coupled chaotic systems, Phys. Rev. E, 51 (1995), 980-994.
doi: 10.1103/PhysRevE.51.980. |
[18] |
S. Sivaprakasam and P. Spencer, Regimes of chaotic synchronization in external-cavity laser diodes, IEEE Journal of Quantum Electronics, 38 (2002), 1155-1161.
doi: 10.1109/JQE.2002.801949. |
[19] |
Q. Song and J. Cao, Global dissipativity analysis on uncertain neural networks with mixed time-varying delays, Chaos, 18 (2008), 043126, 10 pp. |
[20] |
K. Thornburg, M. Moller, R. Roy and T. Carr, Chaos and coherence in coupled lasers, Phys. Rev. E, 55 (1997), 3865.
doi: 10.1103/PhysRevE.55.3865. |
[21] |
J. Wang, Z. Yang, T. Huang and M. Xiao, Local and global exponential synchronization of complex delayed dynamical networks with general topology, Discrete and Continuous Dynamical Systems-Series B, 16 (2011), 393-408.
doi: 10.3934/dcdsb.2011.16.393. |
[22] |
R. Zhen, X. Wu and J. Zhang, "Sliding Model Synchronization Controller Design for Chaotic Neural Network with Time-Varying Delay," Proceedings of the 8th World Congress on Intelligent Control and Automation, China, (2010), 3914-3919.
doi: 10.1109/WCICA.2010.5554977. |
show all references
References:
[1] |
S. Boccaletti, J. Kurths, G. Osipov, D. L. Vallares and C. S. Zhou, The synchronization of chaotic systems, Phys. Rep., 366 (2002), 1-101.
doi: 10.1016/S0370-1573(02)00137-0. |
[2] |
S. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan, "Linear Matrix Inequalities In Systems And Control Theory," SIAM Studies in Applied Mathematics, 15, SIAM, Philadephia, PA, 1994. |
[3] |
J. Cao and J. Lu, Adaptive synchronization of neural networks with or without time-varying delay, Chaos, 16 (2006), 013133, 6 pp. |
[4] |
P. Colet and R. Roy, Digital communication with synchronized chaotic lasers, Opt. Lett., 19 (1994), 2056.
doi: 10.1364/OL.19.002056. |
[5] |
K. Gopalsamy, "Stability and Oscillations in Delay Differential Equations of Population Dynamics," Mathematics and its Applications, 74, Kluwer Academic Publishers Group, Dordrecht, 1992. |
[6] |
H. G. Schuster, ed., "Handbook of Chaos Control: Foundations and Applications," Wiley-VCH, Weinheim, 1999. |
[7] |
H. Huang, G. Feng and Y. Sun, Robust synchronization of chaotic systems subject to parameter uncertainties, Chaos, 19 (2009), 033128.
doi: 10.1063/1.3212940. |
[8] |
T. Huang, C. Li and X. Liu, Synchronization of chaotic systems with delay using intermittent linear state feedback, Chaos, 18 (2008), 033122, 8 pp. |
[9] |
C. Li, G. Feng and X. Liao, Stabilization of nonlinear systems via periodically intermittent control, IEEE Trans. Circuits and Systems II, 54 (2006), 1019-1023. |
[10] |
C. Li, X. Liao and K. Wong, Chaotic lag synchronization of coupled time-delayed systems and its application in secure communication, Physica D, 194 (2004), 187-202.
doi: 10.1016/j.physd.2004.02.005. |
[11] |
X. Liu, T. Chen and W. Lu, Cluster synchronization for linearly coupled complex networks, Journal of Industrial and Management Optimization (JIMO), 7 (2011), 87-101.
doi: 10.3934/jimo.2011.7.87. |
[12] |
J. Lu, J. Cao and D. Ho, Adaptive stabilization and synchronization for chaotic lur’e systems with time-varying delay, IEEE Transactions on Circuits and Systems I: Regular Papers, 55 (2008), 1347-1356.
doi: 10.1109/TCSI.2008.916462. |
[13] |
L. M. Pecora and T. L. Carroll, Synchronization in chaotic systems, Phys. Rev. Lett., 64 (1990), 821-824.
doi: 10.1103/PhysRevLett.64.821. |
[14] |
J. Qing, Projective synchronization of a new hyperchaotic Lorenz system, Physics Letters A, 370 (2007), 40-45.
doi: 10.1016/j.physleta.2007.05.028. |
[15] |
F. Rogister, D. Pieroux, M. Sciamanna, P. Megret and M. Blondel, Anticipating synchronization of two chaotic laser diodes by incoherent optical coupling and its application to secure communications, Optics Communications, 207 (2002), 295-306.
doi: 10.1016/S0030-4018(02)01494-3. |
[16] |
M. Rosenblum and A. Pikovsky, Phase synchronization of chaotic oscillators, Phys. Rev. Lett., 76 (1996), 1804-1807.
doi: 10.1103/PhysRevLett.76.1804. |
[17] |
N. Rulkov and M. Sushchik, Generalized synchronization of chaos in directionally coupled chaotic systems, Phys. Rev. E, 51 (1995), 980-994.
doi: 10.1103/PhysRevE.51.980. |
[18] |
S. Sivaprakasam and P. Spencer, Regimes of chaotic synchronization in external-cavity laser diodes, IEEE Journal of Quantum Electronics, 38 (2002), 1155-1161.
doi: 10.1109/JQE.2002.801949. |
[19] |
Q. Song and J. Cao, Global dissipativity analysis on uncertain neural networks with mixed time-varying delays, Chaos, 18 (2008), 043126, 10 pp. |
[20] |
K. Thornburg, M. Moller, R. Roy and T. Carr, Chaos and coherence in coupled lasers, Phys. Rev. E, 55 (1997), 3865.
doi: 10.1103/PhysRevE.55.3865. |
[21] |
J. Wang, Z. Yang, T. Huang and M. Xiao, Local and global exponential synchronization of complex delayed dynamical networks with general topology, Discrete and Continuous Dynamical Systems-Series B, 16 (2011), 393-408.
doi: 10.3934/dcdsb.2011.16.393. |
[22] |
R. Zhen, X. Wu and J. Zhang, "Sliding Model Synchronization Controller Design for Chaotic Neural Network with Time-Varying Delay," Proceedings of the 8th World Congress on Intelligent Control and Automation, China, (2010), 3914-3919.
doi: 10.1109/WCICA.2010.5554977. |
[1] |
Quan Hai, Shutang Liu. Mean-square delay-distribution-dependent exponential synchronization of chaotic neural networks with mixed random time-varying delays and restricted disturbances. Discrete and Continuous Dynamical Systems - B, 2021, 26 (6) : 3097-3118. doi: 10.3934/dcdsb.2020221 |
[2] |
Carlos Nonato, Manoel Jeremias dos Santos, Carlos Raposo. Dynamics of Timoshenko system with time-varying weight and time-varying delay. Discrete and Continuous Dynamical Systems - B, 2022, 27 (1) : 523-553. doi: 10.3934/dcdsb.2021053 |
[3] |
Yangzi Hu, Fuke Wu. The improved results on the stochastic Kolmogorov system with time-varying delay. Discrete and Continuous Dynamical Systems - B, 2015, 20 (5) : 1481-1497. doi: 10.3934/dcdsb.2015.20.1481 |
[4] |
Juanjuan Huang, Yan Zhou, Xuerong Shi, Zuolei Wang. A single finite-time synchronization scheme of time-delay chaotic system with external periodic disturbance. Mathematical Foundations of Computing, 2019, 2 (4) : 333-346. doi: 10.3934/mfc.2019021 |
[5] |
Xiao Wang, Zhaohui Yang, Xiongwei Liu. Periodic and almost periodic oscillations in a delay differential equation system with time-varying coefficients. Discrete and Continuous Dynamical Systems, 2017, 37 (12) : 6123-6138. doi: 10.3934/dcds.2017263 |
[6] |
Xin-Guang Yang, Jing Zhang, Shu Wang. Stability and dynamics of a weak viscoelastic system with memory and nonlinear time-varying delay. Discrete and Continuous Dynamical Systems, 2020, 40 (3) : 1493-1515. doi: 10.3934/dcds.2020084 |
[7] |
Mokhtar Kirane, Belkacem Said-Houari, Mohamed Naim Anwar. Stability result for the Timoshenko system with a time-varying delay term in the internal feedbacks. Communications on Pure and Applied Analysis, 2011, 10 (2) : 667-686. doi: 10.3934/cpaa.2011.10.667 |
[8] |
Serge Nicaise, Cristina Pignotti, Julie Valein. Exponential stability of the wave equation with boundary time-varying delay. Discrete and Continuous Dynamical Systems - S, 2011, 4 (3) : 693-722. doi: 10.3934/dcdss.2011.4.693 |
[9] |
Baowei Feng, Carlos Alberto Raposo, Carlos Alberto Nonato, Abdelaziz Soufyane. Analysis of exponential stabilization for Rao-Nakra sandwich beam with time-varying weight and time-varying delay: Multiplier method versus observability. Mathematical Control and Related Fields, 2022 doi: 10.3934/mcrf.2022011 |
[10] |
Ruoxia Li, Huaiqin Wu, Xiaowei Zhang, Rong Yao. Adaptive projective synchronization of memristive neural networks with time-varying delays and stochastic perturbation. Mathematical Control and Related Fields, 2015, 5 (4) : 827-844. doi: 10.3934/mcrf.2015.5.827 |
[11] |
Zhen Zhang, Jianhua Huang, Xueke Pu. Pullback attractors of FitzHugh-Nagumo system on the time-varying domains. Discrete and Continuous Dynamical Systems - B, 2017, 22 (10) : 3691-3706. doi: 10.3934/dcdsb.2017150 |
[12] |
Di Wu, Yanqin Bai, Fusheng Xie. Time-scaling transformation for optimal control problem with time-varying delay. Discrete and Continuous Dynamical Systems - S, 2020, 13 (6) : 1683-1695. doi: 10.3934/dcdss.2020098 |
[13] |
Xin-Guang Yang. An Erratum on "Stability and dynamics of a weak viscoelastic system with memory and nonlinear time-varying delay" (Discrete Continuous Dynamic Systems, 40(3), 2020, 1493-1515). Discrete and Continuous Dynamical Systems, 2022, 42 (3) : 1493-1494. doi: 10.3934/dcds.2021161 |
[14] |
Dinh Cong Huong, Mai Viet Thuan. State transformations of time-varying delay systems and their applications to state observer design. Discrete and Continuous Dynamical Systems - S, 2017, 10 (3) : 413-444. doi: 10.3934/dcdss.2017020 |
[15] |
K. Aruna Sakthi, A. Vinodkumar. Stabilization on input time-varying delay for linear switched systems with truncated predictor control. Numerical Algebra, Control and Optimization, 2020, 10 (2) : 237-247. doi: 10.3934/naco.2019050 |
[16] |
Ferhat Mohamed, Hakem Ali. Energy decay of solutions for the wave equation with a time-varying delay term in the weakly nonlinear internal feedbacks. Discrete and Continuous Dynamical Systems - B, 2017, 22 (2) : 491-506. doi: 10.3934/dcdsb.2017024 |
[17] |
Ling Zhang, Xiaoqi Sun. Stability analysis of time-varying delay neural network for convex quadratic programming with equality constraints and inequality constraints. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022035 |
[18] |
Jianping Zhou, Yamin Liu, Ju H. Park, Qingkai Kong, Zhen Wang. Fault-tolerant anti-synchronization control for chaotic switched neural networks with time delay and reaction diffusion. Discrete and Continuous Dynamical Systems - S, 2021, 14 (4) : 1569-1589. doi: 10.3934/dcdss.2020357 |
[19] |
Aowen Kong, Carlos Nonato, Wenjun Liu, Manoel Jeremias dos Santos, Carlos Raposo. Equivalence between exponential stabilization and observability inequality for magnetic effected piezoelectric beams with time-varying delay and time-dependent weights. Discrete and Continuous Dynamical Systems - B, 2022, 27 (6) : 2959-2978. doi: 10.3934/dcdsb.2021168 |
[20] |
Abdelfettah Hamzaoui, Nizar Hadj Taieb, Mohamed Ali Hammami. Practical partial stability of time-varying systems. Discrete and Continuous Dynamical Systems - B, 2022, 27 (7) : 3585-3603. doi: 10.3934/dcdsb.2021197 |
2020 Impact Factor: 1.327
Tools
Metrics
Other articles
by authors
[Back to Top]