zbMATH — the first resource for mathematics

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.

34C60 Qualitative investigation and simulation of ordinary differential equation models
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34D08 Characteristic and Lyapunov exponents of ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
34H05 Control problems involving ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
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), World Scientific Singapore
[5] Lorenz, E.N., Deterministic nonperiodic flow, J atmos sci, 20, 130-141, (1963) · Zbl 1417.37129
[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, 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
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.