A 3-D four-wing attractor and its analysis

Abstract

In this paper, several three dimensional (3-D) four-wing smooth quadratic autonomous chaotic systems are analyzed. It is shown that these systems have a number of similar features. A new 3-D continuous autonomous system is proposed based on these features. The new system can generate a four-wing chaotic attractor with less terms in the system equations. Several basic properties of the new system is analyzed by means of Lyapunov exponents, bifurcation diagrams and Poincare maps. Phase diagrams show that the equilibria are related to the existence of multiple wings.

Active controller design for the GPS of four-wing chaotic systems

“…Wang system is a new four wing chaotic system discovered by Wang et al [44] in 2009 and is given by the 3-D dynamics 1 1 2 3 2 1 2 1 3 3 3 1 2…”

“…Wang four-wing chaotic system ( [44],2008) and Liu four-wing chaotic system ( [45],2009). Lyapunov stability theory [46] has been invoked to prove the main active control results designed in this paper.…”

A four-wing and double-wing 3D chaotic system based on sign function

“…For engineering applications, more complex chaotic attractors will guarantee more randomness and more security. Therefore, many researchers pay attentions to chaotic systems generating complicated attractors, such as multi-layer attractors [7], multi-scroll attractors [8][9][10][11], and multi-wing attractors [12][13][14][15][16][17][18][19][20][21][22][23].…”

“…E-mail address: jinmei liu@126.com subsequently proposed [13][14][15][16][17][18][19][20], including some multi-wing fourdimensional hyperchaotic and chaotic systems [21][22][23]. Although many multi-wing chaotic systems have been developed, most of the systems are realized by linear functions, cross terms and square operations, and other functions are rarely adopted.…”

Simplest 3d Continuous-Time Quadratic Systems as Candidates for Generating Multiscroll Chaotic Attractors

“…In many situations, the existence of several equilibrium points in a dynamical system makes its dynamics more complex and allows some special structures. Examples include the well-known multiscroll attractors ( [Wang, 2009;Qi et al, 2008;Liu & Chen, 2004;Li, 2008;Wang et al, 2009;Lü et al, 2008;Yu et al, 2006;Yu et al, 2008Yu et al, , 2010aWang & Chen, 2012] and references therein) such as chaotic attractors with multiple-merged basins of attraction, scroll grid attractors, and 2n-wing and n × m-wing Lorenz-like attractors. It is remarkable that the vector fields of all these systems are very complex with high dimensions.…”