Synchronization of a Novel Hyperchaotic Complex-Variable System Based on Finite-Time Stability Theory

In this paper, we investigate the finite-time synchronization problem of a novel hyperchaotic complex-variable system which generates 2-, 3- and 4-scroll attractors. Based on the finite-time stability theory, two control strategies are proposed to realize synchronization of the novel hyperchaotic complex-variable system in finite time. Finally, two numerical examples have been provided to illustrate the effectiveness of the theoretical analysis.

[1]  O. Rössler.  An equation for hyperchaos , 1979 .

[2]  Emad E. Mahmoud,et al.  On projective synchronization of hyperchaotic complex nonlinear systems based on passive theory for secure communications , 2013 .

[3]  Vladimir L. Derbov,et al.  Complex Lorenz equations , 1997, Other Conferences.

[4]  Dennis S. Bernstein,et al.  Finite-Time Stability of Continuous Autonomous Systems , 2000, SIAM J. Control. Optim..

[5]  Congxu Zhu,et al.  A novel image encryption scheme based on improved hyperchaotic sequences , 2012 .

[6]  T. Bountis,et al.  Dynamical properties and synchronization of complex non-linear equations for detuned lasers , 2009 .

[7]  Shutang Liu,et al.  Robust adaptive full state hybrid synchronization of chaotic complex systems with unknown parameters and external disturbances , 2012 .

[8]  S. Mascolo,et al.  A system theory approach for designing cryptosystems based on hyperchaos , 1999 .

[9]  S. Boccaletti,et al.  The control of chaos: theory and applications , 2000 .

[10]  Guanrong Chen,et al.  From Chaos To Order Methodologies, Perspectives and Applications , 1998 .

[11]  L. Chua,et al.  Hyper chaos: Laboratory experiment and numerical confirmation , 1986 .

[12]  H. Haken,et al.  Detuned lasers and the complex Lorenz equations: Subcritical and supercritical Hopf bifurcations. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[13]  Tassos Bountis,et al.  Active Control and Global Synchronization of the Complex Chen and lÜ Systems , 2007, Int. J. Bifurc. Chaos.

[14]  U. Vincent,et al.  Finite-time synchronization for a class of chaotic and hyperchaotic systems via adaptive feedback controller , 2011 .

[15]  Mark J. McGuinness,et al.  The real and complex Lorenz equations in rotating fluids and lasers , 1982 .

[16]  Ping Liu,et al.  Adaptive anti-synchronization of chaotic complex nonlinear systems with unknown parameters , 2011 .

[17]  Wei Lin,et al.  Global finite-time stabilization of a class of uncertain nonlinear systems , 2005, Autom..

[18]  Gamal M. Mahmoud,et al.  On Autonomous and nonautonomous Modified hyperchaotic Complex Lü Systems , 2011, Int. J. Bifurc. Chaos.

[19]  Teh-Lu Liao,et al.  An observer-based approach for chaotic synchronization with applications to secure communications , 1999 .

[20]  Manfeng Hu,et al.  Hybrid projective synchronization in a chaotic complex nonlinear system , 2008, Math. Comput. Simul..

[21]  V. Haimo.  Finite time controllers , 1986 .

[22]  Louis M Pecora,et al.  Synchronization of chaotic systems. , 2015, Chaos.

[23]  G. Mahmoud,et al.  A hyperchaotic complex system generating two-, three-, and four-scroll attractors , 2012 .