Chaotic attractors based on unstable dissipative systems via third-order differential equation

In this paper, we present an approach how to yield 1D, 2D and 3D-grid multi-scroll chaotic systems in R3 based on unstable dissipative systems via third-order differential equation. This class of systems is constructed by a switching control law(SCL) changing the equilibrium point of an unstable dissipative system. The switching control law that governs the position of the equilibrium point varies according to the number of scrolls displayed in the attractor.

[2]  Xinghuo Yu,et al.  Generating Grid Multiwing Chaotic Attractors by Constructing Heteroclinic Loops Into Switching Systems , 2011, IEEE Transactions on Circuits and Systems II: Express Briefs.

[3]  Jesus M. Munoz-Pacheco,et al.  Realization of multiscroll chaotic attractors by using current-feedback operational amplifiers , 2010 .

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

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

[6]  C. Tse,et al.  Study of low-frequency bifurcation phenomena of a parallel-connected boost converter system via simple averaged models , 2003 .

[7]  Michael V. Basin,et al.  A family of hyperchaotic multi-scroll attractors in Rn , 2014, Appl. Math. Comput..

[8]  G. Baier,et al.  Maximum hyperchaos in generalized Hénon maps , 1990 .

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

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

[11]  Jun Zhao,et al.  Backstepping design for global stabilization of switched nonlinear systems in lower triangular form under arbitrary switchings , 2010, Autom..

[12]  J. Suykens,et al.  Generation of n-double scrolls (n=1, 2, 3, 4,...) , 1993 .

[13]  Jinhu Lu,et al.  Generating multi-scroll chaotic attractors by thresholding , 2008 .

[14]  Weihua Deng,et al.  Generating multi-directional multi-scroll chaotic attractors via a fractional differential hysteresis system , 2007 .

[15]  I. Campos-Cantón,et al.  Difference map and its electronic circuit realization , 2013 .

[16]  J. Chiou,et al.  Analysis and synthesis of switched nonlinear systems using the T–S fuzzy model , 2010 .

[17]  R Femat,et al.  Multiscroll attractors by switching systems. , 2010, Chaos.

[18]  B. Aguirre‐Hernández,et al.  A polynomial approach for generating a monoparametric family of chaotic attractors via switched linear systems , 2015 .

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

[20]  Ricardo Femat,et al.  Attractors generated from switching unstable dissipative systems. , 2012, Chaos.

[21]  Guanrong Chen,et al.  A family of n-scroll hyperchaotic attractors and their realization , 2007 .

[22]  E. Tlelo-Cuautle,et al.  N-scroll chaotic attractors from saturated function series employing CCII+s , 2010 .

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

[24]  Julien Clinton Sprott,et al.  A New Chaotic Jerk Circuit , 2011, IEEE Transactions on Circuits and Systems II: Express Briefs.

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