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Chaos generalized synchronization of new Mathieu-Van der pol systems with new Duffing-Van der Pol systems as functional system by GYC partial region stability theory. (English) Zbl 1228.93097
Summary: A new strategy by using GYC partial region stability theory is proposed to achieve generalized chaos synchronization. via using the GYC partial region stability theory, the new Lyapunov function used is a simple linear homogeneous function of states and the lower order controllers are much more simple and introduce less simulation error. Numerical simulations are given for new Mathieu-Van der Pol system and new Duffing-Van der Pol system to show the effectiveness of this strategy.

93D15Stabilization of systems by feedback
34H10Chaos control (ODE)
Full Text: DOI
[1] Ott, E.; Grebogi, C.; Yorke, J. A.: Controlling chaos, Phys. rev. Lett. 64, 1196-1199 (1990) · Zbl 0964.37501 · doi:10.1103/PhysRevLett.64.1196
[2] Pyragas, K.: Continuous control of chaos by self-controlling feedback, Phys. lett. A 170, 421-428 (1992)
[3] Chen, Y.; Wu, X.; Gui, Z.: Global synchronization criteria for a class of third-order non-autonomous chaotic systems via linear state error feedback control, Appl. math. Model. 34, 4161-4170 (2010) · Zbl 1201.93045 · doi:10.1016/j.apm.2010.04.013
[4] Femat, R.; Perales, G. S.: On the chaos synchronization phenomenon, Phys. lett. A 262, 50-60 (1999) · Zbl 0936.37010 · doi:10.1016/S0375-9601(99)00667-2
[5] Mu, X.; Pei, L.: Synchronization of the near-identical chaotic systems with the unknown parameters, Appl. math. Model. 34, 1788-1797 (2010) · Zbl 1193.37046 · doi:10.1016/j.apm.2009.09.023
[6] Lu, J.; Wu, X.; Lu, J.: Synchronization of a unified chaotic system and the application in secure communication, Phys. lett. A 305, 365-370 (2002) · Zbl 1005.37012 · doi:10.1016/S0375-9601(02)01497-4
[7] Ge, Z. M.; Chen, C. C.: Phase synchronization of coupled chaotic multiple time scales systems, Chaos solitons fract. 20, 639-647 (2004) · Zbl 1069.34056 · doi:10.1016/j.chaos.2003.08.001
[8] Zhang, W.; Huang, J.; Wei, P.: Weak synchronization of chaotic neural networks with parameter mismatch via periodically intermittent control, Appl. math. Model. 35, 612-620 (2011) · Zbl 1205.93125 · doi:10.1016/j.apm.2010.07.009
[9] Chen, H. K.: Global chaos synchronization of new chaotic systems via nonlinear control, Chaos solitons fract. 23, 1245-1251 (2005) · Zbl 1102.37302 · doi:10.1016/j.chaos.2004.06.040
[10] Yang, X.; Cao, J.: Finite-time stochastic synchronization of complex networks original research article, Appl. math. Model. 34, 3631-3641 (2010) · Zbl 1201.37118 · doi:10.1016/j.apm.2010.03.012
[11] Weng, C. K.; Ray, A.; Dai, X.: Modelling of power plant dynamics and uncertainties for robust control synthesis, Appl. math. Model. 20, 501-512 (1996) · Zbl 0850.93056 · doi:10.1016/0307-904X(95)00169-K
[12] Park, J. H.: Adaptive synchronization of Rössler system with uncertain parameters, Chaos solitons fract. 25, 333-338 (2005) · Zbl 1125.93470 · doi:10.1016/j.chaos.2004.12.007
[13] Park, J. H.: Adaptive synchronization of hyperchaotic Chen system with uncertain parameters, Chaos solitons fract. 26, 959-964 (2005) · Zbl 1093.93537 · doi:10.1016/j.chaos.2005.02.002
[14] Wan, C.; Chang, J.; Yau, H. T.; Chen, J. L.: Nonlinear dynamic analysis of a hybrid squeeze-film damper-mounted rigid rotor lubricated with couple stress fluid and active control, Appl. math. Model. 34, 2493-2507 (2010) · Zbl 1195.70009 · doi:10.1016/j.apm.2009.11.014
[15] Tang, Y.; Fang, J. A.; Xia, M.; Gu, X.: Synchronization of Takagi -- sugeno fuzzy stochastic discrete-time complex networks with mixed time-varying delays, Appl. math. Model. 34, 843-855 (2010) · Zbl 1185.93145 · doi:10.1016/j.apm.2009.07.015
[16] Ge, Z. M.; Leu, W. Y.: Anti-control of chaos of two-degrees-of- freedom louderspeaker system and chaos synchronization of different order systems, Chaos solitons fract. 20, 503-521 (2004) · Zbl 1048.37077 · doi:10.1016/j.chaos.2003.07.001
[17] Ge, Z. M.; Chen, Y. S.: Synchronization of unidirectional coupled chaotic systems via partial stability, Chaos solitons fract. 21, 101-111 (2004) · Zbl 1048.37027 · doi:10.1016/j.chaos.2003.10.004
[18] Ge, Z. M.; Chang, C. M.: Chaos synchronization and parameters identification of single time scale brushless dc motors, Chaos solitons fract. 20, 883-903 (2004) · Zbl 1071.34048 · doi:10.1016/j.chaos.2003.10.005
[19] Ge, Z. M.; Chen, Y. S.: Synchronization of unidirectional coupled chaotic systems via partial stability, Chaos solitons fract. 21, 101-111 (2004) · Zbl 1048.37027 · doi:10.1016/j.chaos.2003.10.004
[20] Ge, Z. M.; Yao, C. W.; Chen, H. K.: Stability on partial region in dynamics, J. chinese soc. Mech. eng. 15, No. 2, 140-151 (1994)
[21] Ge, Z. M.; Chen, H. K.: Three asymptotical stability theorems on partial region with applications, Jpn. J. Appl. phys. 37, 2762-2773 (1998)