A four-wing chaotic attractor generated from a new 3-D quadratic autonomous system

A novel four-wing strange attractor born in bistability

“…Much research has been devoted to searching for new chaotic systems of autonomous ordinary differential equations (ODEs) with particular desired dynamic properties. With improvements in circuit realization technology through the development of integrated circuits, multi-scroll [1,2,3] and multi-wing chaotic systems have aroused special interest, especially four-wing attractors [4,5,6,7,8] and grid multi-wing chaotic systems [9,10,11]. It is known that wing attractors from a chaotic system generally arise from some symmetry, and when that symmetry is broken, the chaotic flow may drop into a different petal of the wing.…”

Generating Chaos in 3d Systems of Quadratic Differential Equations With 1d Exponential Maps

“…Today the most known results devoted to chaotic dynamics in autonomous 3D systems of differential equations are based on the supposition of the existence in these systems of either homoclinic or heteroclinic orbits, and the use of Shilnikov Theorem (see, for example, [Li et al, 2004;Qi et al, 2008;Shang & Han, 2005;Wang, 2009;Zhou et al, 2004;Zheng & Chen, 2006;Zhou & Chen, 2006], and many references cited therein).…”

A 3-D four-wing attractor and its analysis

“…More recently, several different nonlinear functions including switching, hysteresis and saturated functions were utilized for creating chaotic attractors with multi-merged basins of attraction, or with multi-scroll attractors [11][12][13][14]. Note that the aforementioned methods for generating multi-scroll attractors have some common characteristics [15,16]: (i) The nonlinearities of these systems are usually not smooth functions; they are either piecewise-linear continuous functions or discontinuous ones such as the staircase function, switching function, and hysteresis-series function.…”

“…It can be seen that the characteristics of generalized Chua's circuits are different from the generalized Lorenz systems. For example, the nonlinearities of these systems are usually smooth functions, the number of wings is not equal to the number of equilibria and the basic shape of the attractors is a butterfly, called a wing [15,22]. Qi proposed two four-wing chaotic attractors produced by 4-D systems with complicated structure [16,22].…”