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Dynamics and adaptive synchronization of the energy resource system. (English) Zbl 1149.34032
The authors introduce some nonlinear three-dimensional system of ordinary differential equations which is claimed to describe an energy resource system. For this system, apart from analysis of equilibria, they show the existence of chaotic orbits by computing Lyapunov exponents. Afterwards, a control scheme is suggested which allows to synchronize two such coupled systems.

34C60Qualitative investigation and simulation of models (ODE)
34C15Nonlinear oscillations, coupled oscillators (ODE)
34D08Characteristic and Lyapunov exponents
34C28Complex behavior, chaotic systems (ODE)
34H05ODE in connection with control problems
34D05Asymptotic stability of ODE
Full Text: DOI
[1] Gevorgian, V.; Kaiser, M.: Fuel distribution and consumption simulation in the republic of armenia. Simulation 9, 154-167 (1998)
[2] Dong, S.: Energy demand projections based on an uncertain dynamic system modeling approach. Energy sources 7, 443-451 (2000)
[3] Fu, Y.; Tian, L.: Statistical verifying estimation and application of logistic model in the forecast of energy consuming in JiangSu province. J JiangSu univ 13, 17-19 (2001)
[4] Chen, G.; Dong, X.: From chaos to order: methodologies, perspectives and applications. (1998) · Zbl 0908.93005
[5] Lorenz, E. N.: Deterministic nonperiodic flow. J atmos sci 20, 130-141 (1963)
[6] Lü, J.; Chen, G.: A new chaotic attractor coined. Int J bifurcat chaos 12, 659-661 (2002) · Zbl 1063.34510
[7] Lü, J.; Chen, G.; Zhang, S.: The compound structure of a new chaotic attractor. Chaos, solitons & fractals 14, 669-672 (2002) · Zbl 1067.37042
[8] Yu, Y.; Zhang, S.: Hopf bifurcation analysis of the Lü system. Chaos, solitons & fractals 21, 1215-1220 (2004) · Zbl 1061.37029
[9] Bai, E. W.; Lonngren, K. E.: Synchronization of two Lorenz systems using active control. Chaos, solitons & fractals 8, 51-58 (1997) · Zbl 1079.37515
[10] Bai, E. W.; Lonngren, K. E.: Sequential synchronization of two Lorenz systems using active control. Chaos, solitons & fractals 11, 1041-1044 (2000) · Zbl 0985.37106
[11] Elabbasy, E.; Aigiza, H.; El-Dessoky, M.: Adaptive synchronization of Lü system with uncertain parameters. Chaos, solitons & fractals 21, 657-667 (2004) · Zbl 1062.34039
[12] Wang, Y.; Guan, Z.; Wen, X.: Adaptive synchronization for Chen chaotic system with fully unknown parameters. Chaos, solitons & fractals 19, 899-903 (2004) · Zbl 1053.37528
[13] Chen, S.; Lü, J.: Parameter identification and synchronization of chaotic systems based on adaptive control. Phys lett A 299, No. 4, 353-358 (2002) · Zbl 0996.93016
[14] Yassen, M.: Adaptive synchronization of Rössler and Lü system with full uncertain parameters. Chaos, solitons & fractals 23, 1527-1536 (2005) · Zbl 1061.93513