Synchronization of a four-dimensional energy resource system via linear control. (English) Zbl 1221.93238

Summary: The synchronization of a four-dimensional energy resource system is investigated. Four linear control schemes are proposed to synchronize energy resource chaotic system via the back-stepping method. We use simpler controllers to realize a global asymptotical synchronization. In the first three schemes, the sufficient conditions for achieving synchronization of two identical energy resource systems using linear feedback control are derived by using Lyapunov stability theorem. In the fourth scheme, the synchronization condition is obtained by numerical method, in which only one state variable controller is contained. Finally, four numerical simulation examples are performed to verify these results.


93D15 Stabilization of systems by feedback
34H10 Chaos control for problems involving ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
Full Text: DOI


[1] Pecora, L. M.; Carroll, T. L., Synchronization in chaotic systems, Phys Rev Lett, 64, 821-824 (1990) · Zbl 0938.37019
[2] Lu, J.; Cao, J., Adaptive complete synchronization of two identical or different chaotic (hyperchaotic) dynamical systems with fully unknown parameters, Chaos, 15, 043901, 1-10 (2005) · Zbl 1144.37378
[3] Ma, J.; Ying, H. P.; Pu, Z. S., An anti-control scheme for spiral under Lorenz chaotic signal, Chin Phys Lett, 22, 1065-1068 (2005)
[4] Ghosh, D.; Banerjee, S., Adaptive scheme for synchronization-based multiparameter estimation from a single chaotic time series and its applications, Phys Rev E, 78, 056211 (2008)
[5] Ma, J.; Wang, Q. Y.; Jin, W. Y.; Xia, Y. F., Control chaos in the Hindmarsh-Rose neuron by using intermittent feedback with one variable, Chin Phys Lett, 25, 10, 582-3585 (2008)
[6] Wang, Z. L., Anti-synchronization in two non-identical hyperchaotic systems with known or unknown parameters, Commun Nonlinear Sci Numer Simulat, 14, 2366-2372 (2009)
[7] Ma, J.; Jin, W. Y.; Li, Y. L., Chaotic signal-induced dynamics of degenerate optical parametric oscillator, Chaos Soliton Fract, 36, 494-499 (2008)
[8] Park, J. H., Synchronization of Genesio chaotic system via backstepping approach, Chaos Soliton Fract, 27, 1369-1375 (2006) · Zbl 1091.93028
[9] Li, Y. N.; Chen, L.; Cai, Z. S.; Zhao, X. Z., Experimental study of chaos synchronization in the Belousov-Zhabotinsky chemical system, Chaos Soliton Fract, 22, 767-771 (2004) · Zbl 1067.92069
[10] Corron, N. J.; Hahs, D. W., A new approach to communications using chaotic signals, IEEE Trans Circuits Syst, 44, 373-382 (1997) · Zbl 0902.94003
[11] Ims, R. A.; Andreassen, H. P., Spatial synchronization of vole population dynamics by predatory birds, Nature, 408, 194-196 (2000)
[12] Cao, J.; Li, H. X.; Ho, Daniel W. C., Synchronization criteria of Lur’e systems with time-delay feedback control, Chaos Soliton Fract, 23, 1285-1298 (2005) · Zbl 1086.93050
[13] Liang, J.; Cao, J.; Lam, J., Convergence of discrete-time recurrent neural networks with variable delay, Int J Bifurcation Chaos, 15, 581-595 (2005) · Zbl 1098.68107
[14] Ghosh, D.; Chowdhury, A. R.; Saha, P., On the various kinds of synchronization in delayed Duffing-Van der Pol system, Commun Nonlinear Sci Numer Simulat, 13, 4, 790-803 (2008) · Zbl 1221.34196
[15] Sun, M.; Tian, L. X.; Jiang, S.; Xu, J., Feedback control and adaptive control of the energy resource chaotic system, Chaos Soliton Fract, 32, 725-1734 (2007) · Zbl 1129.93403
[16] Sun, M.; Tian, L. X.; Fu, Y.; Qian, W., Dynamics and adaptive synchronization of the energy resource system, Chaos Soliton Fract, 31, 879-888 (2007) · Zbl 1149.34032
[17] Sun, M.; Tian, L. X.; Fu, Y., An energy resources demand-supply system and its dynamical analysis, Chaos Soliton Fract, 32, 168-180 (2007) · Zbl 1133.91524
[18] Sun, M.; Jia, Q.; Tian, L. X., A new four-dimensional energy resources system and its linear feedback control, Chaos Soliton Fract, 39, 101-108 (2009) · Zbl 1197.93122
[19] Sun, M.; Jia, Q.; Tian, L. X., Adaptive control and synchronization of a four-dimensional energy resources system with unknown parameters, Chaos Soliton Fract, 39, 1439-1949 (2009) · Zbl 1197.93100
[20] Jiang, G. P.; Zheng, W. X., An LMI criterion for linear-state-feedback based chaos synchronization of a class of chaotic systems, Chaos Soliton Fract, 26, 437-443 (2005) · Zbl 1153.93390
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.