-
Previous Article
Multistage hierarchical optimization problems with multi-criterion objectives
- JIMO Home
- This Issue
-
Next Article
State estimation for discrete linear systems with observation time-delayed noise
Cluster synchronization for linearly coupled complex networks
1. | The Key Laboratory of Embedded System and Service Computing, Ministry of Education, Department of Computer Science and Technology, Tongji University, Shanghai, 200092, China |
2. | Laboratory of Mathematics for Nonlinear Sciences, School of Mathematical Sciences, Fudan University, Shanghai, 200433, China |
3. | Center for Computational Systems Biology, Laboratory of Mathematics for Nonlinear Sciences, School of Mathematical Sciences, Fudan University, Shanghai, 200433, China |
References:
[1] |
R. Albert and A. Barabsi, Statistical mechanics of complex networks, Rev. Modern Phys., 74 (2002), 47-97.
doi: 10.1103/RevModPhys.74.47. |
[2] |
I. Belykh, V. Belykh and E. Mosekilde, Cluster synchronization modes in an ensemble of coupled chaotic oscillators, Phys. Rev. E, 63 (2001), 036216.
doi: 10.1103/PhysRevE.63.036216. |
[3] |
I. Belykh, V. Belykh, K. Nevidin and M. Hasler, Persistent clusters in lattices of coupled nonidentical chaotic systems, Chaos, 13 (2003), 165-178.
doi: 10.1063/1.1514202. |
[4] |
V. Belykh, I. Belykh and M. Hasler, Connected graph stability method for synchronized coupled chaotic systems, Physica D, 195 (2004), 159-187.
doi: 10.1016/j.physd.2004.03.012. |
[5] |
S. Boccaletti, A. Farini and F. Arecchi, Adaptive synchronization of chaos for secure communication, Phys. Rev. E, 55 (1997), 4979-4981.
doi: 10.1103/PhysRevE.55.4979. |
[6] |
K. Kaneko, Relevance of dynamic clustering to biological networks, Physica D, 75 (1994), 55.
doi: 10.1016/0167-2789(94)90274-7. |
[7] |
Y. Kuang, "Delay Differential Equations in Populaiton Dynamics," Academic Press, New York, 1993. |
[8] |
Y. Li and S. Chen, Optimal traffic signal control for an $M\times N$ traffic network, Journal of Industrial and Management Optimization, 4 (2008), 661-672. |
[9] |
T. Liao and S. Tsai, Adaptive synchronization of chaotic systems and its application to secure communications, Chaos, Solitons and Fractals, 11 (2000), 1387-1396.
doi: 10.1016/S0960-0779(99)00051-X. |
[10] |
X. Liu and T. Chen, Exponential synchronization of the linearly coupled dynamical networks with delays, Chin. Ann. Math. Ser. B, 28 (2007), 737-746.
doi: 10.1007/s11401-006-0194-4. |
[11] |
W. Lu and T. Chen, Synchronization of coupled connected neural networks with delays, IEEE Trans. Circuits Syst.-I, 51 (2004), 2491-2503. |
[12] |
W. Lu and T. Chen, New approach to synchronization analysis of linearly coupled ordinary differential systems, Physica D, 213 (2006), 214-230.
doi: 10.1016/j.physd.2005.11.009. |
[13] |
Z. Ma, Z. Liu and G. Zhang, A new method to realize cluster synchronization in connected chaotic networks, Chao, 16 (2006), 023103. |
[14] |
R. Mirollo and S. Strogatz, Synchronization of pulse-coupled biological oscillators, SIAM J. Appl. Math., 50 (1990), 1645-1662.
doi: 10.1137/0150098. |
[15] |
M. Newman, The structure and function of complex networks, SIAM Rev., 45 (2003), 167-256.
doi: 10.1137/S003614450342480. |
[16] |
L. Pecora and T. Carroll, Master stability functions for synchronized coupled systems, Phys. Rev. Lett., 80 (1998), 2109-2112.
doi: 10.1103/PhysRevLett.80.2109. |
[17] |
A. Pogromsky, G. Santoboni and H. Nijmeijer, An ultimate bound on the trajectories of the Lorenz system and its applications, Nonlinearity, 16 (2003), 1597-1605.
doi: 10.1088/0951-7715/16/5/303. |
[18] |
W. Qin and G. Chen, Coupling schemes for cluster synchronization in coupled Josephson equations, Physica D, 197 (2004), 375-391.
doi: 10.1016/j.physd.2004.07.011. |
[19] |
N. Rulkov, Images of synchronized chaos: experiments with circuits, Chaos, 6 (1996), 262-279.
doi: 10.1063/1.166174. |
[20] |
S. Strogatz, Exploring complex networks, Nature, 410 (2001), 268-276.
doi: 10.1038/35065725. |
[21] |
X. Wang and G. Chen, Synchronization in scale-free dynamical networks: robustness and fragility, IEEE Trans. Circuits Syst. -I, 49 (2002), 54-62. |
[22] |
X. Wang and G. Chen, Synchronization in small-world dynamical networks, Int. J. Bifur. Chaos, 12 (2002), 187-192.
doi: 10.1142/S0218127402004292. |
[23] |
D. Watts and S. Strogatz, Collective dynamics of small-world, Nature, 393 (1998), 440-442.
doi: 10.1038/30918. |
[24] |
G. Wei and Y. Q. Jia, Synchronization-based image edge detection, Europhys. Lett., 59 (2002), 814-819.
doi: 10.1209/epl/i2002-00115-8. |
[25] |
C. Wu, Synchronization in networks of nonlinear dynamical systems coupled via a directed graph, Nonlinearity, 18 (2005), 1057-1064.
doi: 10.1088/0951-7715/18/3/007. |
[26] |
C. Wu and L. Chua, Synchronization in an array of linearly coupled dynamical systems, IEEE Trans. Circuits Syst.-I, 42 (1995), 430-447. |
[27] |
Q. Xie, G. Chen and E. Bollt, Hybrid chaos synchronization and its application in information processing, Math. Comput. Model., 35 (2002), 145-163.
doi: 10.1016/S0895-7177(01)00157-1. |
[28] |
T. Yang and L. O. Chua, Impulsive control and synchronization of nonlinear dynamical systems and application to secure communication, Int. J. Bifur. Chaos, 7 (1997), 645-664.
doi: 10.1142/S0218127497000443. |
show all references
References:
[1] |
R. Albert and A. Barabsi, Statistical mechanics of complex networks, Rev. Modern Phys., 74 (2002), 47-97.
doi: 10.1103/RevModPhys.74.47. |
[2] |
I. Belykh, V. Belykh and E. Mosekilde, Cluster synchronization modes in an ensemble of coupled chaotic oscillators, Phys. Rev. E, 63 (2001), 036216.
doi: 10.1103/PhysRevE.63.036216. |
[3] |
I. Belykh, V. Belykh, K. Nevidin and M. Hasler, Persistent clusters in lattices of coupled nonidentical chaotic systems, Chaos, 13 (2003), 165-178.
doi: 10.1063/1.1514202. |
[4] |
V. Belykh, I. Belykh and M. Hasler, Connected graph stability method for synchronized coupled chaotic systems, Physica D, 195 (2004), 159-187.
doi: 10.1016/j.physd.2004.03.012. |
[5] |
S. Boccaletti, A. Farini and F. Arecchi, Adaptive synchronization of chaos for secure communication, Phys. Rev. E, 55 (1997), 4979-4981.
doi: 10.1103/PhysRevE.55.4979. |
[6] |
K. Kaneko, Relevance of dynamic clustering to biological networks, Physica D, 75 (1994), 55.
doi: 10.1016/0167-2789(94)90274-7. |
[7] |
Y. Kuang, "Delay Differential Equations in Populaiton Dynamics," Academic Press, New York, 1993. |
[8] |
Y. Li and S. Chen, Optimal traffic signal control for an $M\times N$ traffic network, Journal of Industrial and Management Optimization, 4 (2008), 661-672. |
[9] |
T. Liao and S. Tsai, Adaptive synchronization of chaotic systems and its application to secure communications, Chaos, Solitons and Fractals, 11 (2000), 1387-1396.
doi: 10.1016/S0960-0779(99)00051-X. |
[10] |
X. Liu and T. Chen, Exponential synchronization of the linearly coupled dynamical networks with delays, Chin. Ann. Math. Ser. B, 28 (2007), 737-746.
doi: 10.1007/s11401-006-0194-4. |
[11] |
W. Lu and T. Chen, Synchronization of coupled connected neural networks with delays, IEEE Trans. Circuits Syst.-I, 51 (2004), 2491-2503. |
[12] |
W. Lu and T. Chen, New approach to synchronization analysis of linearly coupled ordinary differential systems, Physica D, 213 (2006), 214-230.
doi: 10.1016/j.physd.2005.11.009. |
[13] |
Z. Ma, Z. Liu and G. Zhang, A new method to realize cluster synchronization in connected chaotic networks, Chao, 16 (2006), 023103. |
[14] |
R. Mirollo and S. Strogatz, Synchronization of pulse-coupled biological oscillators, SIAM J. Appl. Math., 50 (1990), 1645-1662.
doi: 10.1137/0150098. |
[15] |
M. Newman, The structure and function of complex networks, SIAM Rev., 45 (2003), 167-256.
doi: 10.1137/S003614450342480. |
[16] |
L. Pecora and T. Carroll, Master stability functions for synchronized coupled systems, Phys. Rev. Lett., 80 (1998), 2109-2112.
doi: 10.1103/PhysRevLett.80.2109. |
[17] |
A. Pogromsky, G. Santoboni and H. Nijmeijer, An ultimate bound on the trajectories of the Lorenz system and its applications, Nonlinearity, 16 (2003), 1597-1605.
doi: 10.1088/0951-7715/16/5/303. |
[18] |
W. Qin and G. Chen, Coupling schemes for cluster synchronization in coupled Josephson equations, Physica D, 197 (2004), 375-391.
doi: 10.1016/j.physd.2004.07.011. |
[19] |
N. Rulkov, Images of synchronized chaos: experiments with circuits, Chaos, 6 (1996), 262-279.
doi: 10.1063/1.166174. |
[20] |
S. Strogatz, Exploring complex networks, Nature, 410 (2001), 268-276.
doi: 10.1038/35065725. |
[21] |
X. Wang and G. Chen, Synchronization in scale-free dynamical networks: robustness and fragility, IEEE Trans. Circuits Syst. -I, 49 (2002), 54-62. |
[22] |
X. Wang and G. Chen, Synchronization in small-world dynamical networks, Int. J. Bifur. Chaos, 12 (2002), 187-192.
doi: 10.1142/S0218127402004292. |
[23] |
D. Watts and S. Strogatz, Collective dynamics of small-world, Nature, 393 (1998), 440-442.
doi: 10.1038/30918. |
[24] |
G. Wei and Y. Q. Jia, Synchronization-based image edge detection, Europhys. Lett., 59 (2002), 814-819.
doi: 10.1209/epl/i2002-00115-8. |
[25] |
C. Wu, Synchronization in networks of nonlinear dynamical systems coupled via a directed graph, Nonlinearity, 18 (2005), 1057-1064.
doi: 10.1088/0951-7715/18/3/007. |
[26] |
C. Wu and L. Chua, Synchronization in an array of linearly coupled dynamical systems, IEEE Trans. Circuits Syst.-I, 42 (1995), 430-447. |
[27] |
Q. Xie, G. Chen and E. Bollt, Hybrid chaos synchronization and its application in information processing, Math. Comput. Model., 35 (2002), 145-163.
doi: 10.1016/S0895-7177(01)00157-1. |
[28] |
T. Yang and L. O. Chua, Impulsive control and synchronization of nonlinear dynamical systems and application to secure communication, Int. J. Bifur. Chaos, 7 (1997), 645-664.
doi: 10.1142/S0218127497000443. |
[1] |
Yu-Jing Shi, Yan Ma. Finite/fixed-time synchronization for complex networks via quantized adaptive control. Electronic Research Archive, 2021, 29 (2) : 2047-2061. doi: 10.3934/era.2020104 |
[2] |
Chol-Ung Choe, Thomas Dahms, Philipp Hövel, Eckehard Schöll. Control of synchrony by delay coupling in complex networks. Conference Publications, 2011, 2011 (Special) : 292-301. doi: 10.3934/proc.2011.2011.292 |
[3] |
Juan Cao, Fengli Ren, Dacheng Zhou. Asymptotic and finite-time cluster synchronization of neural networks via two different controllers. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022005 |
[4] |
Jin-Liang Wang, Zhi-Chun Yang, Tingwen Huang, Mingqing Xiao. Local and global exponential synchronization of complex delayed dynamical networks with general topology. Discrete and Continuous Dynamical Systems - B, 2011, 16 (1) : 393-408. doi: 10.3934/dcdsb.2011.16.393 |
[5] |
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 |
[6] |
M. Syed Ali, L. Palanisamy, Nallappan Gunasekaran, Ahmed Alsaedi, Bashir Ahmad. Finite-time exponential synchronization of reaction-diffusion delayed complex-dynamical networks. Discrete and Continuous Dynamical Systems - S, 2021, 14 (4) : 1465-1477. doi: 10.3934/dcdss.2020395 |
[7] |
Yong Zhao, Shanshan Ren. Synchronization for a class of complex-valued memristor-based competitive neural networks(CMCNNs) with different time scales. Electronic Research Archive, 2021, 29 (5) : 3323-3340. doi: 10.3934/era.2021041 |
[8] |
Kun Liang, Wangli He, Yang Yuan, Liyu Shi. Synchronization for singularity-perturbed complex networks via event-triggered impulsive control. Discrete and Continuous Dynamical Systems - S, 2022 doi: 10.3934/dcdss.2022068 |
[9] |
Ramasamy Saravanakumar, Yang Cao, Ali Kazemy, Quanxin Zhu. Sampled-data based extended dissipative synchronization of stochastic complex dynamical networks. Discrete and Continuous Dynamical Systems - S, 2022 doi: 10.3934/dcdss.2022082 |
[10] |
Tianhu Yu, Jinde Cao, Chuangxia Huang. Finite-time cluster synchronization of coupled dynamical systems with impulsive effects. Discrete and Continuous Dynamical Systems - B, 2021, 26 (7) : 3595-3620. doi: 10.3934/dcdsb.2020248 |
[11] |
Samuel Bowong, Jean Luc Dimi. Adaptive synchronization of a class of uncertain chaotic systems. Discrete and Continuous Dynamical Systems - B, 2008, 9 (2) : 235-248. doi: 10.3934/dcdsb.2008.9.235 |
[12] |
Daniel M. N. Maia, Elbert E. N. Macau, Tiago Pereira, Serhiy Yanchuk. Synchronization in networks with strongly delayed couplings. Discrete and Continuous Dynamical Systems - B, 2018, 23 (8) : 3461-3482. doi: 10.3934/dcdsb.2018234 |
[13] |
Sujit Nair, Naomi Ehrich Leonard. Stable synchronization of rigid body networks. Networks and Heterogeneous Media, 2007, 2 (4) : 597-626. doi: 10.3934/nhm.2007.2.597 |
[14] |
Inmaculada Leyva, Irene Sendiña-Nadal, Stefano Boccaletti. Explosive synchronization in mono and multilayer networks. Discrete and Continuous Dynamical Systems - B, 2018, 23 (5) : 1931-1944. doi: 10.3934/dcdsb.2018189 |
[15] |
Tingwen Huang, Guanrong Chen, Juergen Kurths. Synchronization of chaotic systems with time-varying coupling delays. Discrete and Continuous Dynamical Systems - B, 2011, 16 (4) : 1071-1082. doi: 10.3934/dcdsb.2011.16.1071 |
[16] |
Michael Gekhtman, Michael Shapiro, Serge Tabachnikov, Alek Vainshtein. Higher pentagram maps, weighted directed networks, and cluster dynamics. Electronic Research Announcements, 2012, 19: 1-17. doi: 10.3934/era.2012.19.1 |
[17] |
Yannick Holle, Michael Herty, Michael Westdickenberg. New coupling conditions for isentropic flow on networks. Networks and Heterogeneous Media, 2020, 15 (4) : 605-631. doi: 10.3934/nhm.2020016 |
[18] |
Seung-Yeal Ha, Dohyun Kim, Jaeseung Lee, Se Eun Noh. Emergence of aggregation in the swarm sphere model with adaptive coupling laws. Kinetic and Related Models, 2019, 12 (2) : 411-444. doi: 10.3934/krm.2019018 |
[19] |
Junhyeok Byeon, Seung-Yeal Ha, Hansol Park. Asymptotic interplay of states and adaptive coupling gains in the Lohe Hermitian sphere model. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022007 |
[20] |
Shirin Panahi, Sajad Jafari. New synchronization index of non-identical networks. Discrete and Continuous Dynamical Systems - S, 2021, 14 (4) : 1359-1373. doi: 10.3934/dcdss.2020371 |
2020 Impact Factor: 1.801
Tools
Metrics
Other articles
by authors
[Back to Top]