On Autonomous and nonautonomous Modified hyperchaotic Complex Lü Systems

In this paper autonomous and nonautonomous modified hyperchaotic complex Lu systems are proposed. Our systems have been generated by using state feedback and complex periodic forcing. The basic properties of these systems are studied. Parameters range for hyperchaotic attractors to exist are calculated. These systems have very rich dynamics in a wide range of parameters. The analytical results are tested numerically and excellent agreement is found. A circuit diagram is designed for one of these hyperchaotic complex systems and simulated using Matlab/Simulink to verify the hyperchaotic behavior.

[1]  Emad E. Mahmoud,et al.  A Hyperchaotic Complex Chen System and its Dynamics , 2007 .

[2]  Silvano Cincotti,et al.  Hyperchaotic behaviour of two bi‐directionally coupled Chua's circuits , 2002, Int. J. Circuit Theory Appl..

[3]  Mark J. McGuinness,et al.  The real and complex Lorenz equations and their relevance to physical systems , 1983 .

[4]  Guanrong Chen,et al.  Generating Hyperchaos via State Feedback Control , 2005, Int. J. Bifurc. Chaos.

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

[6]  Sara Dadras,et al.  Four-scroll hyperchaos and four-scroll chaos evolved from a novel 4D nonlinear smooth autonomous system , 2010 .

[7]  An-Pei Wang,et al.  Controlling hyperchaos of the Rossler system , 1999 .

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

[9]  Guanrong Chen,et al.  On the security of the Yi-Tan-Siew chaotic cipher , 2004, IEEE Transactions on Circuits and Systems II: Express Briefs.

[10]  Gamal M. Mahmoud,et al.  Chaotic Behavior And Chaos Control For A Class Of Complex Partial Differential Equations , 2001 .

[11]  Simin Yu,et al.  Generating hyperchaotic Lü attractor via state feedback control , 2006 .

[12]  Tassos Bountis,et al.  The Dynamics of Systems of Complex Nonlinear oscillators: a Review , 2004, Int. J. Bifurc. Chaos.

[13]  Gamal M. Mahmoud,et al.  Chaotic and hyperchaotic attractors of a complex nonlinear system , 2008 .

[14]  Emad E. Mahmoud,et al.  ANALYSIS OF HYPERCHAOTIC COMPLEX LORENZ SYSTEMS , 2008 .

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

[16]  Zuolei Wang.  Projective synchronization of hyperchaotic Lü system and Liu system , 2010 .

[17]  N. Abraham,et al.  Global stability properties of the complex Lorenz model , 1996 .

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

[19]  Guangyi Wang,et al.  A new modified hyperchaotic Lü system , 2006 .

[20]  Saverio Mascolo,et al.  SYNCHRONIZING HIGH DIMENSIONAL CHAOTIC SYSTEMS VIA EIGENVALUE PLACEMENT WITH APPLICATION TO CELLULAR NEURAL NETWORKS , 1999 .

[21]  Paul Mandel,et al.  Influence of detuning on the properties of laser equations , 1985 .

[22]  Guoyuan Qi,et al.  A four-wing hyper-chaotic attractor and transient chaos generated from a new 4-D quadratic autonomous system , 2010 .

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

[24]  Emad E. Mahmoud,et al.  On the hyperchaotic complex Lü system , 2009 .

[25]  Mary Ainsworth.  On Security , 2000 .

[26]  Guanrong Chen,et al.  Controlling a unified chaotic system to hyperchaotic , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.