On globally exponential stable complete synchronization of nearly identical hyperchaotic systems via linear active control

College of Applied Sciences Nizwa, Ministry of Higher Education, Sultanate of Oman. iak_2000plus@yahoo.com, azizan.s@uum.edu.my, adyda@uum.edu.my, dmsinfinite@gmail.com Abstract. This paper reports the globally exponential stable complete synchronization behavior between two identical hyperchaotic systems using a modified linear active control technique. Based on the Lyapunov stability theory and using the linear active control technique, some easily sufficient conditions are derived to determine a suitable controller gain. The conditions are then applied to achieve globally exponential stable complete synchronization between two identical Lorenz type hyperchaotic systems. Numerical simulation results are furnished to validate the theoretical findings. The effect of the controller gain is our under discussions. Keyword. Complete synchronization, Linear active control, Lyapunov stability theory, Hyperchaotic system

[1]  Li Xu,et al.  Finite‐Time Synchronization of General Complex Dynamical Networks , 2015 .

[2]  Mohammad Shahzad,et al.  Global chaos synchronization of new chaotic system using linear active control , 2015, Complex..

[3]  Binoy Krishna Roy,et al.  Synchronization and anti-synchronization of Lu and Bhalekar–Gejji chaotic systems using nonlinear active control , 2014 .

[4]  Mohammad Shahzad,et al.  A Research on the Synchronization of Two Novel Chaotic Systems Based on a Nonlinear Active Control Algorithm , 2014 .

[5]  Pagavathigounder Balasubramaniam,et al.  Synchronization of chaotic systems using feedback controller: An application to Diffie–Hellman key exchange protocol and ElGamal public key cryptosystem , 2014 .

[6]  Ying Wang,et al.  Study on spatiotemporal chaos synchronization among complex networks with diverse structures , 2014 .

[7]  Chi-Ching Yang,et al.  One input control of exponential synchronization for a four-dimensional chaotic system , 2013, Appl. Math. Comput..

[8]  O. Olusola,et al.  Global Stability and Synchronization Criteria of Linearly Coupled Gyroscope , 2013 .

[9]  Zhen Jia,et al.  Adaptive Lag Synchronization of Lorenz Chaotic System with Uncertain Parameters , 2012 .

[10]  Guanrong Chen,et al.  A new hyperchaotic Lorenz‐type system: Generation, analysis, and implementation , 2011, Int. J. Circuit Theory Appl..

[11]  T. Aldemir,et al.  Synchronization of different chaotic systems using generalized active control , 2009, 2009 International Conference on Electrical and Electronics Engineering - ELECO 2009.

[12]  A. N. Njah,et al.  Synchronization and Anti-synchronization of double hump Duffing-Van der Pol Oscillators via Active Control , 2009 .

[13]  Uchechukwu E. Vincent,et al.  Synchronization of identical and non-identical 4-D chaotic systems using active control , 2008 .

[14]  Anita C. Faul,et al.  Non-linear systems , 2006 .

[15]  Pei Yu,et al.  Study of Globally Exponential Synchronization for the Family of RÖssler Systems , 2006, Int. J. Bifurc. Chaos.

[16]  Yao-Chen Hung,et al.  Synchronization of two different systems by using generalized active control , 2002 .

[17]  H.-K. Chen.  CHAOS AND CHAOS SYNCHRONIZATION OF A SYMMETRIC GYRO WITH LINEAR-PLUS-CUBIC DAMPING , 2002 .

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