Synchronization of Chaotic Energy Resource System


Taking a four-dimensional energy resources demand-supply system between the East and West of China, this paper discusses its chaotic behavior, and via the unilateral coupling method we lead the system to synchronization successfully. But not all the values of coupling coefficient can lead to synchronization. The values of coupling coefficient have a range. By calculating the maximal relative Lyapunov exponents’ spectrum, we gained the value range of coupling coefficients. Within the value range, the two coupling systems can achieve synchronization, otherwise can’t. Further more, the values of coupling coefficient are in connection with the chaos synchronizing time. At last, we get the relationship of coupling coefficients and chaos synchronizing time.

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T. Wang, H. Xie and A. Xie, "Synchronization of Chaotic Energy Resource System," Applied Mathematics, Vol. 4 No. 1, 2013, pp. 58-63. doi: 10.4236/am.2013.41011.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] C. F. Huang, K. H. Cheng and J. J. Yan, “Robust Chaos Synchronization of Four-Dimensional Energy Resource Systems Subject to Unmatched Uncertainties,” Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 6, 2009, pp. 2784-2792. doi:10.1016/j.cnsns.2008.09.017
[2] J. A. Lu, X. Q. Wu and J. H. Lu, “Synchronization of a Unified Chaotic System and the Application in Secure Communication,” Physics Letters, Vol. 305, No. 6, 2002, pp. 365-370. doi:10.1016/S0375-9601(02)01497-4
[3] S. A. Ammour, S. Djennoune and M. Bettayed, “A Sliding Mode Control for Linear Fractional Systems with Input and State Delays,” Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 5, 2009, pp. 2310-2318. doi:10.1016/j.cnsns.2008.05.011
[4] B. L. Feng, B. Han and H. H. Dong, “Integrable Couplings and Hamiltonian Structures of the L-Hierarchy and the T-Hierarchy,” Communications in Nonlinear Science and Numerical Simulation, Vol. 13, No. 7, 2008, pp. 1264-1271. doi:10.1016/j.cnsns.2007.02.004
[5] S. Bowong, “Adaptive Synchronization between Two Different Chaotic Dynamical Systems,” Communications in Nonlinear Science and Numerical Simulation, Vol. 12, No. 6, 2007, pp. 976-985. doi:10.1016/j.cnsns.2005.10.003
[6] S. M. Guo, L. S. Shieh, G. Chen and C. F. Lin, “Effective Chaotic Orbit Tracker: A Prediction-Based Digital Redesign Approach,” IEEE Transactions on Circuits and Systems, Vol. 47, No. 11, 2000, pp. 1557-1560. doi:10.1109/81.895324
[7] M. Sun, Q. Jia and L. X. Tian, “A New Four-Dimensional Energy Resources System and Its Linear Feedback Control,” Chaos Solitons & Fractals, Vol. 39, No. 1, 2009, pp. 101-108. doi:10.1016/j.chaos.2007.01.125
[8] G. R. Chen, et al., “From Chaos to Order,” World Scientific Publishing, Singapore City, 1997.
[9] T. B. Wang, T. F. Qin and G. Z. Chen, “Coupled Synchronization of Hyperchaotic Systems,” Acta Physica Sinica, Vol, 50, No. 11, 2001, pp. 1851-1855.

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