THE GENERATION AND ANALYSIS OF A NEW FOUR-DIMENSIONAL HYPERCHAOTIC SYSTEM

A new four-dimensional continuous autonomous hyperchaotic system is considered. It possesses two parameters, and each equation of it has one quadratic cross product term. Some basic properties of it are studied. The dynamic behaviors of it are analyzed by the Lyapunov exponent (LE) spectrum, bifurcation diagrams, phase portraits, and Poincare sections. The system has larger hyperchaotic region. When it is hyperchaotic, the two positive LE are both large and they are both larger than 1 if the system parameters are taken appropriately.

[1]  A. Tamasevicius,et al.  Hyperchaos in coupled Colpitts oscillators , 2003 .

[2]  Atsushi Uchida,et al.  Generalized synchronization of chaos: experiments on a two-mode microchip laser with optoelectronic feedback , 2004 .

[3]  Guanrong Chen,et al.  On a Generalized Lorenz Canonical Form of Chaotic Systems , 2002, Int. J. Bifurc. Chaos.

[4]  Svetoslav Nikolov,et al.  Occurrence of regular, chaotic and hyperchaotic behavior in a family of modified Rossler hyperchaotic systems , 2004 .

[5]  K. Thamilmaran,et al.  Hyperchaos in a Modified Canonical Chua's Circuit , 2004, Int. J. Bifurc. Chaos.

[6]  Ming-Jyi Jang,et al.  Sliding mode control of hyperchaos in Rössler systems , 2002 .

[7]  Svetoslav Nikolov,et al.  Hyperchaos–chaos–hyperchaos transition in modified Rössler systems , 2006 .

[8]  Guanrong Chen,et al.  Hyperchaos evolved from the generalized Lorenz equation , 2005, Int. J. Circuit Theory Appl..

[9]  Zhenya Yan,et al.  Controlling hyperchaos in the new hyperchaotic Chen system , 2005, Appl. Math. Comput..

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

[11]  Guanrong Chen,et al.  YET ANOTHER CHAOTIC ATTRACTOR , 1999 .

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

[13]  Guanrong Chen,et al.  Analysis of a new chaotic system , 2005 .

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

[15]  K. Grygiel,et al.  Hyperchaos in second-harmonic generation of light , 1998 .

[16]  Giuseppe Grassi,et al.  New 3D-scroll attractors in hyperchaotic Chua's Circuits Forming a Ring , 2003, Int. J. Bifurc. Chaos.

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

[18]  Guanrong Chen,et al.  A HYPERCHAOS GENERATED FROM CHEN'S SYSTEM , 2006 .

[19]  C. Chui,et al.  A symmetric image encryption scheme based on 3D chaotic cat maps , 2004 .

[20]  Jinhu Lu,et al.  A New Chaotic Attractor Coined , 2002, Int. J. Bifurc. Chaos.

[21]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

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

[23]  H. N. Agiza,et al.  Chaos Synchronization of Two Coupled Dynamos Systems with Unknown System Parameters , 2004 .