A hyperchaotic complex system generating two-, three-, and four-scroll attractors

In this paper we propose a hyperchaotic complex system which generates 2-, 3- and 4-scroll attractors. Lyapunov exponents are calculated to observe hyperchaotic behavior. The stability analysis of the trivial fixed point is studied. Its dynamics are more rich in the sense that our system exhibits both chaotic and hyperchaotic attractors as well as periodic and quasi-periodic solutions, and solutions that approach fixed points. Bifurcation parameter diagrams are presented. Controlling hyperchaotic attractors of this system is investigated. The Lyapunov exponents are calculated to verify the control performance.

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

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

[3]  Kestutis Pyragas.  Continuous control of chaos by self-controlling feedback , 1992 .

[4]  Pérez,et al.  Extracting messages masked by chaos. , 1995, Physical review letters.

[5]  A. J. Lichtenberg,et al.  Nonlinear feedback for control of chaos , 1996 .

[6]  Chi-Chuan Hwang,et al.  A new feedback control of a modified Chua's circuit system , 1996 .

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

[8]  Gamal M. Mahmoud,et al.  Strange attractors and chaos control in periodically forced complex Duffing's oscillators , 2001 .

[9]  Johan A. K. Suykens,et al.  n-scroll chaos generators: a simple circuit model , 2001 .

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

[11]  O. Rössler,et al.  Hyperchaos of arbitrary order generated by a single feedback circuit, and the emergence of chaotic walks. , 2004, Chaos.

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

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

[14]  Guanrong Chen,et al.  Generating Multiscroll Chaotic Attractors: Theories, Methods and Applications , 2006 .

[15]  GUANRONG CHEN,et al.  Four-Wing attractors: from Pseudo to Real , 2006, Int. J. Bifurc. Chaos.

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

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

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

[19]  SIMIN YU,et al.  Generation of n × M-scroll attractors under a Chua-Circuit Framework , 2007, Int. J. Bifurc. Chaos.

[20]  Bradley J. Bazuin,et al.  Generation of a Four-Wing Chaotic Attractor by Two Weakly-Coupled Lorenz Systems , 2008, Int. J. Bifurc. Chaos.

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

[22]  G. Grassi.  Novel four-wing and eight-wing attractors using coupled chaotic Lorenz systems , 2008 .

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

[24]  Guanrong Chen,et al.  A four-wing chaotic attractor generated from a new 3-D quadratic autonomous system , 2008 .

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

[26]  Sara Dadras,et al.  A novel three-dimensional autonomous chaotic system generating two, three and four-scroll attractors , 2009 .

[27]  Lin Wang,et al.  3-scroll and 4-scroll chaotic attractors generated from a new 3-D quadratic autonomous system , 2009 .

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

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

[30]  Ping Wang,et al.  Comparison of feedback control methods for a hyperchaotic Lorenz system , 2010 .

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

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