Synchronization of a chaotic finance system

Synchronization strategies of a three-dimensional chaotic finance system are investigated in this paper. Based on Lyapunov stability theory and Routh-Hurwitz criteria, some effective controllers are designed for the global asymptotic synchronization on different conditions. When the system parameters are known, the hybrid feedback control and a method based on special matrix structure are adopted respectively, to realize the synchronization of the chaotic finance system. When the parameters are unknown, the active control is extended and introduced to realize the synchronization. Numerical simulations show the validity and feasibility of the synchronization schemes.

[1]  Xiao-Jing Wang,et al.  Alternating and Synchronous Rhythms in Reciprocally Inhibitory Model Neurons , 1992, Neural Computation.

[2]  Jianbing Hu,et al.  Synchronizing chaotic systems using control based on a special matrix structure and extending to fractional chaotic systems , 2010 .

[3]  Yi Li,et al.  Adaptive control and synchronization of a novel hyperchaotic system with uncertain parameters , 2008, Appl. Math. Comput..

[4]  Chuandong Li,et al.  Chaotic lag synchronization of coupled time-delayed systems and its applications in secure communication , 2004 .

[5]  Haiwu Rong,et al.  Chaos synchronization of two stochastic Duffing oscillators by feedback control , 2007 .

[6]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[7]  Yoshiki Kuramoto,et al.  Chemical Oscillations, Waves, and Turbulence , 1984, Springer Series in Synergetics.

[8]  Leon O. Chua,et al.  Chaos Synchronization in Chua's Circuit , 1993, J. Circuits Syst. Comput..

[9]  Dequan Li,et al.  Connecting the Lorenz and Chen systems via nonlinear control , 2009 .

[10]  Tian Li.  Adaptive synchronization of non-linear chaotic finance system , 2005 .

[11]  Li-Xin Yang,et al.  Chaos synchronization in autonomous chaotic system via hybrid feedback control , 2009 .

[12]  M. T. Yassen,et al.  Adaptive control and synchronization of a modified Chua's circuit system , 2003, Appl. Math. Comput..

[13]  Congxu Zhu,et al.  Adaptive synchronization of two novel different hyperchaotic systems with partly uncertain parameters , 2009, Appl. Math. Comput..

[14]  Heng-Hui Chen.  Global synchronization of chaotic systems via linear balanced feedback control , 2007, Appl. Math. Comput..

[15]  B. R. Nana Nbendjo,et al.  Active control of extended Van der Pol equation , 2007 .

[16]  Xiao Fan Wang,et al.  Global Synchronization of a Class of Chaotic Systems with a Scalar Transmitted Signal , 2004, Int. J. Bifurc. Chaos.

[17]  Mohd. Salmi Md. Noorani,et al.  Application of the differential transformation method for the solution of the hyperchaotic Rössler system , 2009 .

[18]  Dong-Choon Lee,et al.  DC-bus voltage control of three-phase AC/DC PWM converters using feedback linearization , 2000 .

[19]  Ma Junhai,et al.  Study for the bifurcation topological structure and the global complicated character of a kind of nonlinear finance system (I) , 2001 .

[20]  Bernd Blasius,et al.  Complex dynamics and phase synchronization in spatially extended ecological systems , 1999, Nature.

[21]  Vinod Patidar,et al.  Suppression of chaos using mutual coupling , 2002 .

[22]  Antonina Pirrotta,et al.  Active controlled structural systems under delta-correlated random excitation: Linear and nonlinear case , 2006 .