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Fastest synchronized network and synchrony on the Julia set of complex-valued coupled map lattices
1. | Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan, Taiwan, Taiwan |
References:
[1] |
E. Ahmed, H. A. Abdusalam and E. S. Fahmy, On telegraph reaction diffusion and coupled map lattice in some biological systems, Int. J. Mod. Phys. C, 12 (2001), 717-726.
doi: 10.1142/S0129183101001936. |
[2] |
M. Barahona and L. M. Pecora, Synchronization in small-world systems, Phys. Rev. Lett., 89 (2002), 054101.
doi: 10.1103/PhysRevLett.89.054101. |
[3] |
Å. Brännström and D. J. T. Sumpter, Coupled map lattice approximations for spatially explicit individual-based models of ecology, Bulletin Math. Biol., 67 (2005), 663-682.
doi: 10.1016/j.bulm.2004.09.006. |
[4] | |
[5] |
R. L. Devaney, An Introduction to Chaotic Dynamical Systems, $2^{nd}$ edition, Addison-Wesley, California, 1989. |
[6] |
K. S. Fink, G. Johnson, T. Carroll, D. Mar and L. Pecora, Three coupled oscillators as a universal probe of synchronization stability in coupled oscillator arrays, Phys. Rev. Lett., 61 (2000), 5080-5090.
doi: 10.1103/PhysRevE.61.5080. |
[7] |
G. Hu, J. Yang and W. Liu, Instability and controllability of linearly coupled oscillators: Eigenvalue analysis, Phys. Rev. E, 58 (1998), 4440-4453.
doi: 10.1103/PhysRevE.58.4440. |
[8] |
J. Jost and M. P. Joy, Spectral properties and synchronization in coupled map lattices, Phys. Rev. E, 65 (2002), 016201, 9pp.
doi: 10.1103/PhysRevE.65.016201. |
[9] |
J. Juang and Y. H. Liang, Synchronous chaos in coupled map lattices with general connectivity topology, SIAM J. Appl. Dyn. Syst., 7 (2008), 755-765.
doi: 10.1137/070705179. |
[10] |
K. Kaneko, Overview of coupled map lattices, Chaos, 2 (1992), 279-282.
doi: 10.1063/1.165869. |
[11] |
X. Li and G. Chen, Synchronization and desynchronization of complex dynamical networks: An engineering viewpoint, IEEE Trans. Circuits Syst. I, 50 (2003), 1381-1390.
doi: 10.1109/TCSI.2003.818611. |
[12] |
W. W. Lin and Y. Q. Wang, Chaotic synchronization in coupled map lattices with periodic boundary conditions, SIAM J. Appl. Dyn. Syst., 1 (2002), 175-189.
doi: 10.1137/S1111111101395410. |
[13] |
W. W. Lin and Y. Q. Wang, Proof of synchronized chaotic behaviors in coupled map lattices, Int. J. Bifur. and Chaos, 21 (2011), 1493-1500.
doi: 10.1142/S0218127411029069. |
[14] |
L. M. Pecora and T. L. Carroll, Master stability functions for synchronized coupled systems, Phys. Rev. Lett., 80 (1998), 2109-2112.
doi: 10.1103/PhysRevLett.80.2109. |
[15] |
C. Robinson, Dynamical Systems: Stability, Symbolic Dynamics, and Chaos, $2^{nd}$ edition, CRC Press, Florida, 1999. |
[16] |
M. Zhan, G. Hu and J. Yang, Synchronization of chaos in coupled systems, Phys. Rev. E, 62 (2000), 2963-2966.
doi: 10.1103/PhysRevE.62.2963. |
show all references
References:
[1] |
E. Ahmed, H. A. Abdusalam and E. S. Fahmy, On telegraph reaction diffusion and coupled map lattice in some biological systems, Int. J. Mod. Phys. C, 12 (2001), 717-726.
doi: 10.1142/S0129183101001936. |
[2] |
M. Barahona and L. M. Pecora, Synchronization in small-world systems, Phys. Rev. Lett., 89 (2002), 054101.
doi: 10.1103/PhysRevLett.89.054101. |
[3] |
Å. Brännström and D. J. T. Sumpter, Coupled map lattice approximations for spatially explicit individual-based models of ecology, Bulletin Math. Biol., 67 (2005), 663-682.
doi: 10.1016/j.bulm.2004.09.006. |
[4] | |
[5] |
R. L. Devaney, An Introduction to Chaotic Dynamical Systems, $2^{nd}$ edition, Addison-Wesley, California, 1989. |
[6] |
K. S. Fink, G. Johnson, T. Carroll, D. Mar and L. Pecora, Three coupled oscillators as a universal probe of synchronization stability in coupled oscillator arrays, Phys. Rev. Lett., 61 (2000), 5080-5090.
doi: 10.1103/PhysRevE.61.5080. |
[7] |
G. Hu, J. Yang and W. Liu, Instability and controllability of linearly coupled oscillators: Eigenvalue analysis, Phys. Rev. E, 58 (1998), 4440-4453.
doi: 10.1103/PhysRevE.58.4440. |
[8] |
J. Jost and M. P. Joy, Spectral properties and synchronization in coupled map lattices, Phys. Rev. E, 65 (2002), 016201, 9pp.
doi: 10.1103/PhysRevE.65.016201. |
[9] |
J. Juang and Y. H. Liang, Synchronous chaos in coupled map lattices with general connectivity topology, SIAM J. Appl. Dyn. Syst., 7 (2008), 755-765.
doi: 10.1137/070705179. |
[10] |
K. Kaneko, Overview of coupled map lattices, Chaos, 2 (1992), 279-282.
doi: 10.1063/1.165869. |
[11] |
X. Li and G. Chen, Synchronization and desynchronization of complex dynamical networks: An engineering viewpoint, IEEE Trans. Circuits Syst. I, 50 (2003), 1381-1390.
doi: 10.1109/TCSI.2003.818611. |
[12] |
W. W. Lin and Y. Q. Wang, Chaotic synchronization in coupled map lattices with periodic boundary conditions, SIAM J. Appl. Dyn. Syst., 1 (2002), 175-189.
doi: 10.1137/S1111111101395410. |
[13] |
W. W. Lin and Y. Q. Wang, Proof of synchronized chaotic behaviors in coupled map lattices, Int. J. Bifur. and Chaos, 21 (2011), 1493-1500.
doi: 10.1142/S0218127411029069. |
[14] |
L. M. Pecora and T. L. Carroll, Master stability functions for synchronized coupled systems, Phys. Rev. Lett., 80 (1998), 2109-2112.
doi: 10.1103/PhysRevLett.80.2109. |
[15] |
C. Robinson, Dynamical Systems: Stability, Symbolic Dynamics, and Chaos, $2^{nd}$ edition, CRC Press, Florida, 1999. |
[16] |
M. Zhan, G. Hu and J. Yang, Synchronization of chaos in coupled systems, Phys. Rev. E, 62 (2000), 2963-2966.
doi: 10.1103/PhysRevE.62.2963. |
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