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Complex spatiotemporal behavior in a chain of one-way nonlinearly coupled elements
1. | Bogolyubov Institute for Theoretical Physics, Metrologichna str. 14 B, 01413, Kiev, Ukraine |
2. | Department of Mathematics, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark, Denmark |
3. | Department of Applied Mathematics and Statistics, University of the Basque Country, E-48080 Bilbao, Spain |
4. | Department of Informatics and Mathematical Modeling & Department of Physics, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark |
5. | Toyota Central R&D Labs, Inc., Nagakute, 480-1192 Aichi, Japan, Japan |
6. | Department of Mathematics and Computer Science, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark |
References:
[1] |
M. Abramowitz and I. Stegun, "Handbook of Mathematical Functions," Dover Publications, Inc., New York, 1972. |
[2] |
M. Bando, K. Hasebe, A. Nakayama, A. Shibata and Y. Sugiyama, Dynamical model of traffic congestion and numerical simulation, Phys. Rev. E, 51 (1995), 1035-1042.
doi: 10.1103/PhysRevE.51.1035. |
[3] |
A. R. Bulsara, V. In, A. Kho, A. Palacios, P. Longhini, J. D. Neff, G. Anderson, C. Obra, S. Baglio and B. Ando, Exploiting nonlinear dynamics in a coupled-core fluxgate magnetometer, Meas. Sci. Technol., 19 (2008), 075203-075221.
doi: 10.1088/0957-0233/19/7/075203. |
[4] |
A. H. Cohen, P. J. Holmes and R. H. Rand, The nature of the coupling between segmental oscillators and the lamprey spinal generator for locomotion: A mathematical model,, J. Math. Biol., 13 (): 345.
doi: 10.1007/BF00276069. |
[5] |
Yu. B. Gaididei, R. Berkemer, J. G. Caputo, P. L. Christiansen, A. Kawamoto, T. Shiga, M. P. Sørensen and J. Starke, Analytical solutions of jam pattern formation on a ring for a class of optimal velocity traffic models, New Journal of Phys., 11 (2009), 073012-073030.
doi: 10.1088/1367-2630/11/7/073012. |
[6] |
J. Guckenheimer and P. Holmes, "Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields," Springer-Verlag, New York, Heidelberg, Berlin, 1997. |
[7] |
D. Helbing, Traffic and related self-driven many-particle systems, Rev. Modern Phys., 73 (2001), 1067-1141.
doi: 10.1103/RevModPhys.73.1067. |
[8] |
V. In, A. Kho, J. D. Neff, A. Palacios, P. Longhini and B. K. Meadows, Experimental observation of multifrequency patterns in arrays of coupled nonlinear oscillators, Phys. Rev. Lett., 91 (2003), 244101-244104.
doi: 10.1103/PhysRevLett.91.244101. |
[9] |
V. In, A. Palacios, P. Longhini, A. Kho, J. D. Neff, S. Baglio and B. Ando, Complex behavior in driven unidirectionally coupled overdamped Duffing oscillators, Phys. Rev. E, 73 (2006), 066121-066129.
doi: 10.1103/PhysRevE.73.066121. |
[10] |
B. S. Kerner, "The Physics of Traffic: Empirical Freeway Pattern Features, Engineering Applications, and Theory," Springer, Heidelberg, 2004. |
[11] |
B. S. Kerner, "Introduction to Modern Traffic Flow Theory and Control. The Long Road to Three-Phase Traffic Theory," Springer, Berlin, 2009.
doi: 10.1007/978-3-642-02605-8. |
[12] |
T. Nagatani, The physics of traffic jams, Rep. Prog. Phys., 65 (2002), 1331-1386.
doi: 10.1088/0034-4885/65/9/203. |
[13] |
C. M. A. Pinto and M. Golubitsky, Central pattern generators for bipedal locomotion, J. Math. Biol., 53 (2006), 474-489.
doi: 10.1007/s00285-006-0021-2. |
[14] |
Yu. Sugiyama, M. Fukui, M. Kikuchi, K. Hasebe, A. Nakayama, K. Nishinari, S. Tadaki and S. Yukawa, Traffic jams without bottlenecks-experimental evidence for the physical mechanism of the formation of a jam, New Journal of Phys., 10 (2008), 033001-033007.
doi: 10.1088/1367-2630/10/3/033001. |
[15] |
A. Takamatsu, R. Tanaka, T. Nakagaki, T. Fujii, and I. Endo, Spatiotemporal symmetry in rings of coupled biological oscillators of Physarum plasmoidal slime mold, Phys. Rev. Lett., 87 (2001), 078102-078105.
doi: 10.1103/PhysRevLett.87.078102. |
[16] |
A. Takamatsu, R. Tanaka and T. Fujii, Hidden symmetry in chains of biological coupled oscillators, Phys. Rev. Lett., 92 (2004), 228102-228105.
doi: 10.1103/PhysRevLett.92.228102. |
[17] |
K. van der Weele, G. Kannelopulos, C. Tsiavos and D. van der Meer, Transient granular shock waves and upstream motion on a staircase, Phys. Rev. E, 80 (2009), 011305 (16 pages). |
[18] |
S. Wiggins, "Introduction to Applied Dynamical Systems and Chaos," Springer-Verlag, New York, Heidelberg, Berlin, 1990. |
[19] |
D. E. Wolf, M. Schreckenberg and A. Bachem (ed), "Traffic and Granular Flow," World Scientific, Singapore, 1996. |
[20] |
M. Yamamoto, Y. Nomura and Y. Sugiyama, Dissipative system with asymmetric interaction and Hopf bifurcation, Phys. Rev. E, 80 (2009), 026203-026209.
doi: 10.1103/PhysRevE.80.026203. |
show all references
References:
[1] |
M. Abramowitz and I. Stegun, "Handbook of Mathematical Functions," Dover Publications, Inc., New York, 1972. |
[2] |
M. Bando, K. Hasebe, A. Nakayama, A. Shibata and Y. Sugiyama, Dynamical model of traffic congestion and numerical simulation, Phys. Rev. E, 51 (1995), 1035-1042.
doi: 10.1103/PhysRevE.51.1035. |
[3] |
A. R. Bulsara, V. In, A. Kho, A. Palacios, P. Longhini, J. D. Neff, G. Anderson, C. Obra, S. Baglio and B. Ando, Exploiting nonlinear dynamics in a coupled-core fluxgate magnetometer, Meas. Sci. Technol., 19 (2008), 075203-075221.
doi: 10.1088/0957-0233/19/7/075203. |
[4] |
A. H. Cohen, P. J. Holmes and R. H. Rand, The nature of the coupling between segmental oscillators and the lamprey spinal generator for locomotion: A mathematical model,, J. Math. Biol., 13 (): 345.
doi: 10.1007/BF00276069. |
[5] |
Yu. B. Gaididei, R. Berkemer, J. G. Caputo, P. L. Christiansen, A. Kawamoto, T. Shiga, M. P. Sørensen and J. Starke, Analytical solutions of jam pattern formation on a ring for a class of optimal velocity traffic models, New Journal of Phys., 11 (2009), 073012-073030.
doi: 10.1088/1367-2630/11/7/073012. |
[6] |
J. Guckenheimer and P. Holmes, "Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields," Springer-Verlag, New York, Heidelberg, Berlin, 1997. |
[7] |
D. Helbing, Traffic and related self-driven many-particle systems, Rev. Modern Phys., 73 (2001), 1067-1141.
doi: 10.1103/RevModPhys.73.1067. |
[8] |
V. In, A. Kho, J. D. Neff, A. Palacios, P. Longhini and B. K. Meadows, Experimental observation of multifrequency patterns in arrays of coupled nonlinear oscillators, Phys. Rev. Lett., 91 (2003), 244101-244104.
doi: 10.1103/PhysRevLett.91.244101. |
[9] |
V. In, A. Palacios, P. Longhini, A. Kho, J. D. Neff, S. Baglio and B. Ando, Complex behavior in driven unidirectionally coupled overdamped Duffing oscillators, Phys. Rev. E, 73 (2006), 066121-066129.
doi: 10.1103/PhysRevE.73.066121. |
[10] |
B. S. Kerner, "The Physics of Traffic: Empirical Freeway Pattern Features, Engineering Applications, and Theory," Springer, Heidelberg, 2004. |
[11] |
B. S. Kerner, "Introduction to Modern Traffic Flow Theory and Control. The Long Road to Three-Phase Traffic Theory," Springer, Berlin, 2009.
doi: 10.1007/978-3-642-02605-8. |
[12] |
T. Nagatani, The physics of traffic jams, Rep. Prog. Phys., 65 (2002), 1331-1386.
doi: 10.1088/0034-4885/65/9/203. |
[13] |
C. M. A. Pinto and M. Golubitsky, Central pattern generators for bipedal locomotion, J. Math. Biol., 53 (2006), 474-489.
doi: 10.1007/s00285-006-0021-2. |
[14] |
Yu. Sugiyama, M. Fukui, M. Kikuchi, K. Hasebe, A. Nakayama, K. Nishinari, S. Tadaki and S. Yukawa, Traffic jams without bottlenecks-experimental evidence for the physical mechanism of the formation of a jam, New Journal of Phys., 10 (2008), 033001-033007.
doi: 10.1088/1367-2630/10/3/033001. |
[15] |
A. Takamatsu, R. Tanaka, T. Nakagaki, T. Fujii, and I. Endo, Spatiotemporal symmetry in rings of coupled biological oscillators of Physarum plasmoidal slime mold, Phys. Rev. Lett., 87 (2001), 078102-078105.
doi: 10.1103/PhysRevLett.87.078102. |
[16] |
A. Takamatsu, R. Tanaka and T. Fujii, Hidden symmetry in chains of biological coupled oscillators, Phys. Rev. Lett., 92 (2004), 228102-228105.
doi: 10.1103/PhysRevLett.92.228102. |
[17] |
K. van der Weele, G. Kannelopulos, C. Tsiavos and D. van der Meer, Transient granular shock waves and upstream motion on a staircase, Phys. Rev. E, 80 (2009), 011305 (16 pages). |
[18] |
S. Wiggins, "Introduction to Applied Dynamical Systems and Chaos," Springer-Verlag, New York, Heidelberg, Berlin, 1990. |
[19] |
D. E. Wolf, M. Schreckenberg and A. Bachem (ed), "Traffic and Granular Flow," World Scientific, Singapore, 1996. |
[20] |
M. Yamamoto, Y. Nomura and Y. Sugiyama, Dissipative system with asymmetric interaction and Hopf bifurcation, Phys. Rev. E, 80 (2009), 026203-026209.
doi: 10.1103/PhysRevE.80.026203. |
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