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A new four-dimensional energy resources system and its linear feedback control. (English) Zbl 1197.93122
Summary: This paper reports a new four-dimensional energy resources chaotic system. The system is obtained by adding a new variable to a three-dimensional energy resource demand-supply system established for two regions of China. The dynamics behavior of the system will be analyzed by means of Lyapunov exponents and bifurcation diagrams. Linear feedback control methods are used to suppress chaos to unstable equilibrium or unstable periodic orbits. Numerical simulations are presented to show these results. Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

93C95Applications of control theory
Full Text: DOI
[1] Rösslor, O. E.: An equation for continuous chaos, Phys lett A 57, 397-398 (1976)
[2] Lorenz, E. N.: Deterministic nonperiodic flow, J atmos sci 20, 130-141 (1963)
[3] Arneodo, A.; Coullet, P.; Tresser, C.: A possible new mechanism for the onset of turbulence, Phys lett A 81A, 197-201 (1981) · Zbl 0485.58013
[4] Chen, G.; Ueta, T.: Yet another chaotic attractor, Int J bifurcat chaos 9, 1465-1466 (1999) · Zbl 0962.37013 · doi:10.1142/S0218127499001024
[5] Ueta, T.; Chen, G.: Bifurcation analysis of Chen’s equation, Int J bifurcat chaos 10, 1917-1931 (2000) · Zbl 1090.37531 · doi:10.1142/S0218127400001183
[6] Lü, J. H.; Chen, G.; Celikovsky, S.: Bridge the gap between the Lorenz system and the Chen system, Int J bifurcat chaos 12, 2917-2926 (2002) · Zbl 1043.37026 · doi:10.1142/S021812740200631X
[7] Mei, Sun; Lixin, Tian: An energy resources demand -- supply system and its dynamical analysis, Chaos, solitons & fractals 32, 168 (2007) · Zbl 1133.91524 · doi:10.1016/j.chaos.2005.10.085
[8] Mei, Sun; Lixin, Tian; Ying, Fu; Wei, Qian: Dynamics and adaptive synchronization of the energy resource system, Chaos, solitons & fractals 31, 879 (2007) · Zbl 1149.34032 · doi:10.1016/j.chaos.2005.10.035
[9] Mei, Sun; Lixin, Tian; Jian, Yin: Hopf bifurcation analysis of the energy resource chaotic system, International journal of nonlinear science 1, 49 (2006)
[10] Mei, Sun; Lixin, Tian; Shumin, Jiang; Jun, Xu: Feedback control and adaptive control of the energy resource chaotic system, Chaos, solitons & fractals 32, 1725-1734 (2007) · Zbl 1129.93403 · doi:10.1016/j.chaos.2005.12.008
[11] Chen, G.; Dong, X.: On feedback control of chaotic continuous time systems, IEEE trans circ syst 40, 591 (1993) · Zbl 0800.93758 · doi:10.1109/81.244908