This paper investigates the modified projective synchronization problem of two hyperchaotic systems in the presence of unknown and/or uncertain system parameters. Based on the Lyapunov stability theory two control laws are proposed to make the states of two identical hyperchaotic systems asymptotically synchronized. Numerical simulations are presented to show the effectiveness of the proposed schemes.
Bowong S., Kakmeni FMM and Tchawoua C. ( 2005) Chaos control and synchronization of a class of uncertain chaotic systems. Journal of Vibration and Control11: 1007-1024.
2.
Chen YS, Hwang RR and Chang CC (2010) Adaptive impulsive synchronization of uncertain chaotic systems. Physics Letters A374: 2254-2258.
3.
Huang J. ( 2008) Adaptive synchronization between different hyperchaotic systems with fully uncertain parameters. Physics Letters A372: 4799-4804.
4.
Kocarev L. and Parlitz U. ( 1996) Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems. Physical Review Letters76: 1816-1819.
5.
Li GH ( 2006) Projective synchronization of chaotic system using backstepping control. Chaos, Solitons & Fractals29: 490-494.
6.
Li GH ( 2007) Modified projective synchronization of chaotic system . Chaos, Solitons & Fractals32: 1786-1790.
7.
Luo RZ ( 2008) Adaptive function project synchronization of R Össler hyperchaotic system with uncertain parameters. Physics Letters A372: 3667-3671.
8.
Ma ZJ, Liu ZR and Zhang G. ( 2006) A new method to realize cluster synchronization in connected chaotic networks. Chaos16: 023103.
9.
Mainieri R. and Rehacek J. ( 1999) Projective synchronization in three-dimensional chaotic systems. Physical Review Letters82: 3042-3045.
10.
Njah AN and Vincent UE(2009) Synchronization and anti-synchronization of chaos in an extended Bonh Ö ffer-van der Pol oscillator using active control. Journal of Sound and Vibration319: 41-49.
11.
Pecora LM and Carroll TL ( 1990) Synchronization in chaotic systems. Physical Review Letters64: 821-824.
12.
Rosenblum MG, Pikovsky AS and Kurths J. ( 1996) Phase synchronization of chaotic oscillators. Physical Review Letters76: 1804-1807.
13.
Taherionl S. and Lai YC ( 1999) Observability of lag synchronization of coupled chaotic oscillators. Physical Review E59: 6247-6250.
14.
Tavazoei MS and Haeri M. ( 2007) Determination of active sliding mode controller parameters in synchronizing different chaotic systems. Chaos, Solitons & Fractals32: 583-591.
15.
Wang FQ and Liu CX ( 2007) Synchronization of unified chaotic system based on passive control. Physica D225: 55-60.
16.
Wang XY and Song MJ(2009) Synchronization of the fractional order hyperchaos Lorenz systems with activation feedback control. Communications in Nonlinear Science and Numerical Simulation14: 3351-3357.
17.
Yassen MT ( 2008) Synchronization hyperchaos of hyperchaotic systems . Chaos, Solitons & Fractals37: 465-475.
18.
Yu WW and Cao JD ( 2007) Adaptive synchronization and lag synchronization of uncertain dynamical system with time delay based on parameter identification . Physica A375: 467-482.
19.
Yu YG and Li HX ( 2008) The synchronization of fractional order R Össler hyperchaotic systems. Physica A387: 1393-1403.
20.
Zhang G., Liu ZR and Zhang JB ( 2008) Adaptive synchronization of a class of continuous chaotic systems with uncertain parameters. Physics Letters A372: 447-450.
21.
Zhang XH and Shen K. ( 1999) The control action of the periodic perturbation on a hyperchaotic system. Acta Physica Sinica8: 651-656.
22.
Zhu CX ( 2010) Generalized projective synchronization and parameters estimation of two new hyperchaotic systems with fully uncertain parameters . International Journal of Modern Physics C21: 249-259.