Generation of $n\times m$-Wing Lorenz-Like Attractors From a Modified Shimizu–Morioka Model

This paper explores the generation of n- and n times m-wing Lorenz-type attractors from a modified Shimizu-Morioka system. The basic idea is to increase the number of index-2 equilibrium points by introducing a multisegment quadratic function and a stair function in the 2-D state-space of the system. The design is verified by both simulation and experiment, where multiwing attractors over a grid can be clearly observed.

[1]  Xinghuo Yu,et al.  Generating 3-D multi-scroll chaotic attractors: A hysteresis series switching method , 2004, Autom..

[2]  T. Shimizu,et al.  On the bifurcation of a symmetric limit cycle to an asymmetric one in a simple model , 1980 .

[3]  Guanrong Chen,et al.  Secure synchronization of a class of chaotic systems from a nonlinear observer approach , 2005, IEEE Transactions on Automatic Control.

[4]  Leon O. Chua,et al.  A family of n-scroll attractors from a generalized Chua's circuit , 1997 .

[5]  R. Robinson,et al.  Homoclinic bifurcation to a transitive attractor of Lorenz type , 1989 .

[6]  J. Suykens,et al.  Experimental confirmation of 3- and 5-scroll attractors from a generalized Chua's circuit , 2000 .

[7]  Johan A. K. Suykens,et al.  Families of scroll Grid attractors , 2002, Int. J. Bifurc. Chaos.

[8]  Guanrong Chen,et al.  A general multiscroll Lorenz system family and its realization via digital signal processors. , 2006, Chaos.

[9]  Simin Yu,et al.  Tetrapterous butterfly attractors in modified Lorenz systems , 2009 .

[10]  Guanrong Chen,et al.  Generation of n-scroll attractors via sine function , 2001 .

[11]  Marek Rychlik,et al.  Lorenz attractors through Šil'nikov-type bifurcation. Part I , 1990, Ergodic Theory and Dynamical Systems.

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

[13]  Guanrong Chen,et al.  Multi-wing butterfly attractors from the modified Lorenz systems , 2008, 2008 IEEE International Symposium on Circuits and Systems.

[14]  C. Sparrow The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors , 1982 .

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

[16]  L. Shilnikov,et al.  NORMAL FORMS AND LORENZ ATTRACTORS , 1993 .

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

[18]  L. Chua,et al.  The double scroll family , 1986 .

[19]  Henry Leung,et al.  Experimental verification of multidirectional multiscroll chaotic attractors , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[20]  Guanrong Chen,et al.  Multifolded torus chaotic attractors: design and implementation. , 2007, Chaos.

[21]  Kim-Fung Man,et al.  A Systematic Approach to Generating n-scroll attractors , 2002, Int. J. Bifurc. Chaos.

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

[23]  M. Viana What’s new on lorenz strange attractors? , 2000 .

[24]  Xinghuo Yu,et al.  Multi-parameter modulation for secure communication via Lorenz chaos , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[25]  Jinde Cao,et al.  New communication schemes based on adaptive synchronization. , 2007, Chaos.

[26]  Rabinder N Madan,et al.  Chua's Circuit: A Paradigm for Chaos , 1993, Chua's Circuit.