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Chaos control and hybrid projective synchronization for a class of new chaotic systems. (English) Zbl 1236.93073
Summary: The problems on chaos control and hybrid projective synchronization for a class of new chaotic systems are considered. First, new 4D chaotic systems are proposed by introducing an additional state into a 3D quadratic chaotic system and the states of the systems corresponding to the different ranges of parameter b are exhibited. Second, a single scalar adaptive feedback controller for chaos control of the systems is presented. Third, hybrid projective synchronization (HPS) of two of the chaotic systems with parameters in different conditions are investigated by presenting adaptive feedback control strategies with adaptive parameter update laws and considering controller simplification to achieve complete synchronization. Finally, numerical simulations are demonstrated to verify the effectiveness of the strategies.
93B52Feedback control
34H10Chaos control (ODE)
37N35Dynamical systems in control
93A13Hierarchical systems
[1]Sparrow, C.: The Lorenz equations: bifurcations, chaos, and strange attractors, (1982)
[2]Ueta, T.; Chen, G.: Bifurcation analysis of Chen’s attractor, Internat. J. Bifur. chaos 10, 1917-1931 (2000) · Zbl 1090.37531 · doi:10.1142/S0218127400001183
[3]Lü, J. H.; Chen, G.: A new chaotic attractor coined, Internat. J. Bifur. chaos 12, 659-661 (2002) · Zbl 1063.34510 · doi:10.1142/S0218127402004620
[4]Lü, J. H.; Chen, G.; Cheng, D.; Celikovsky, S.: Bridge the gap between the Lorenz system and the Chen system, Internat. J. Bifur. chaos 12, 2917-2926 (2002) · Zbl 1043.37026 · doi:10.1142/S021812740200631X
[5]Tigan, G.; Opris, D.: Analysis of a 3D chaotic system, Chaos solitons fractals 36, 1315-1319 (2008) · Zbl 1148.37027 · doi:10.1016/j.chaos.2006.07.052
[6]Chen, Z.; Yang, Y.; Qi, G.; Yuan, Z.: A novel hyperchaos system only with one equilibrium, Phys. lett. A 360, 696-701 (2007)
[7]Ott, E.; Grebogi, G.; York, J. A.: Controlling chaos, Phys. rev. Lett. 64, 1196-1199 (1990) · Zbl 0964.37501 · doi:10.1103/PhysRevLett.64.1196
[8]Pecora, L. M.; Carroll, T. L.: Synchronization in chaotic system, Phys. rev. Lett. 64, 821-825 (1990)
[9]Moskalenko, O. I.; Koronovskii, A. A.; Hramov, A. E.: Generalized synchronization of chaos for secure communication: remarkable stability to noise, Phys. lett. A 374, 2925-2931 (2010)
[10]Liu, M. Q.: Optimal exponential synchronization of general chaotic delayed neural networks: an LMI approach, Neural netw. 22, 949-957 (2009)
[11]Upadhyay, R. K.; Rai, V.: Complex dynamics and synchronization in two non-identical chaotic ecological systems, Chaos solitons fractals 40, 2233-2241 (2009) · Zbl 1198.37133 · doi:10.1016/j.chaos.2007.10.016
[12]Gray, R. T.; Robinson, P. A.: Stability and synchronization of random brain networks with a distribution of connection strengths, Neurocomputing 71, 1373-1387 (2008)
[13]Yu, W. W.; Cao, J. D.: Adaptive synchronization and lag synchronization of uncertain dynamical system with time delay based on parameter identification, Physica A 375, 467-482 (2007)
[14]Diebner, H. H.; Grond, F.: Usability of synchronization for cognitive modeling, Chaos solitons fractals 25, 905-910 (2005) · Zbl 1125.37323 · doi:10.1016/j.chaos.2005.02.035
[15]Balasubramaniam, P.; Chandran, R.; Theesar, S. Jeeva Sathya: Synchronization of chaotic nonlinear continuous neural networks with time-varying delay, Cogn. neuropsychol. (2011)
[16]Odibat, Z.: A note on phase synchronization in coupled chaotic fractional order systems, Nonlinear anal.-real. (2011)
[17]Liu, S.; Liu, P.: Adaptive anti-synchronization of chaotic complex nonlinear systems with unknown parameters, Nonlinear anal.-real. 12, 3046-3055 (2011) · Zbl 1231.37020 · doi:10.1016/j.nonrwa.2011.05.006
[18]Ghosh, D.; Banerjee, S.; Roychowdhury, A.: Generalized and projective synchronization in modulated time-delayed systems, Phys. lett. A 374, 2143-2149 (2010)
[19]Hu, M.; Xu, Z.; Zhang, R.; Hu, A.: Adaptive full state hybrid projective synchronization of chaotic systems with the same and different order, Phys. lett. A 365, 315-327 (2007)
[20]Chee, C. Y.; Xu, D.: Chaos-based M-ary digital communication technique using controlled projective synchronisation, IEE proc., circuits devices syst. 153, 357-360 (2006)
[21]Park, J. H.: Controlling chaotic systems via nonlinear feedback control, Chaos solitons fractals 23, 1049-1054 (2005) · Zbl 1061.93508 · doi:10.1016/j.chaos.2004.06.016
[22]Chen, H. K.: Global chaos synchronization of new chaotic systems via nonlinear control, Chaos solitons fractals 23, 1245-1251 (2005) · Zbl 1102.37302 · doi:10.1016/j.chaos.2004.06.040
[23]Tang, R. A.; Liu, Y. L.; Xue, J. K.: An extended active control for chaos synchronization, Phys. lett. A 373, 1449-1454 (2009) · Zbl 1228.34078 · doi:10.1016/j.physleta.2009.02.036
[24]Nbendjo, B. R. Nana; Tchoukuegno, R.; Woafo, P.: Active control with delay of vibration and chaos in a double-well Duffing oscillator, Chaos solitons fractals 18, 345-353 (2003) · Zbl 1057.37081 · doi:10.1016/S0960-0779(02)00681-1
[25]Njah, A. N.: Synchronization via active control of identical and non-identical chaotic oscillators with external excitation, J. sound vib. 327, 322-332 (2009)
[26]Li, W.: Adaptive chaos control and synchronization in only locally Lipschitz systems, Phys. lett. A 372, 3195-3200 (2008) · Zbl 1220.34080 · doi:10.1016/j.physleta.2008.01.038
[27]Salarieh, H.; Alasty, A.: Adaptive chaos synchronization in Chua’s systems with noisy parameters, Math. comput. Simulation 79, 233-241 (2008) · Zbl 1166.34029 · doi:10.1016/j.matcom.2007.11.007
[28]Ge, Z. M.; Li, S. C.; Li, S. Y.; Chang, C. M.: Pragmatical adaptive chaos control from a new double van der Pol system to a new double Duffing system, Appl. math. Comput. 203, 513-522 (2008) · Zbl 1152.93037 · doi:10.1016/j.amc.2008.05.011
[29]Salarieh, H.; Shahrokhi, M.: Adaptive synchronization of two different chaotic systems with time varying unknown parameters, Chaos solitons fractals 37, 125-136 (2008) · Zbl 1147.93397 · doi:10.1016/j.chaos.2006.08.038
[30]Pourmahmood, M.; Khanmohammadi, S.; Alizadeh, G.: Synchronization of two different uncertain chaotic systems with unknown parameters using a robust adaptive sliding mode controller, Commun. nonlinear sci. Numer. simul. 16, 2853-2868 (2011) · Zbl 1221.93131 · doi:10.1016/j.cnsns.2010.09.038
[31]Aghababa, M. P.; Khanmohammadi, S.; Alizadeh, G.: Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique, Appl. math. Model. 35, 3080-3091 (2011) · Zbl 1219.93023 · doi:10.1016/j.apm.2010.12.020
[32]Li, Y.; Wong, K. W.; Liao, X. F.; Li, C. D.: On impulsive control for synchronization and its application to the nuclear spin generator system, Nonlinear anal.-real. 10, 1712-1716 (2009) · Zbl 1160.49036 · doi:10.1016/j.nonrwa.2008.02.011
[33]Chen, J.; Liu, H.; Lu, J.; Zhang, Q. J.: Projective and lag synchronization of a novel hyperchaotic system via impulsive control, Commun. nonlinear sci. Numer. simul. 16, 2033-2040 (2011) · Zbl 1221.93104 · doi:10.1016/j.cnsns.2010.07.027
[34]Slotine, J. E.; Li, W.: Applied nonlinear control, (1991) · Zbl 0753.93036
[35]Zhang, H. G.; Liu, D. R.; Wang, Z. L.: Controlling chaos: suppression, synchronization and chaotification, (2009)