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Study on Congestion and Bursting in Small-World Networks with Time Delay from the Viewpoint of Nonlinear Dynamics |
| LIU Yan1,2**, LIU Li-Guang2, WANG Hang2 |
1School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072
2Xi'an Shaangu Power Co. LTD, Xi'an 710075 |
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| Cite this article: |
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LIU Yan, LIU Li-Guang, WANG Hang 2012 Chin. Phys. Lett. 29 060504 |
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Abstract The small-world network model represented by a set of evolution equations with time delay is used to investigate the nonlinear dynamics of networks, and the nature of instability phenomena in traffic, namely, congestion and bursting in the networks, are studied and explained from bifurcation analysis. Then, the governing equation in the vector field is further reduced into a map, and the ensuing period-doubling bifurcation, sequence of period-doubling bifurcation and period-3 are studied intuitively. The existence of chaos is verified numerically. In particular, the influences of time delay on the nonlinear dynamics are presented. The results show that there are a rich variety of nonlinear dynamics related to the intermittency of the traffic flows in the system, and the results can gain a fundamental understanding of the instability in the networks, and the time delay can be used as a key parameter in the control of the systems.
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Received: 28 November 2011
Published: 31 May 2012
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| PACS: |
05.10.-a
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(Computational methods in statistical physics and nonlinear dynamics)
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05.45.-a
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(Nonlinear dynamics and chaos)
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