Topological horseshoe analysis and the circuit implementation for a four-wing chaotic attractor

Abstract

The paper first analyzes a newly reported three-dimensional four-wing chaotic attractor, and observes all kinds of attractors, including periodic and chaotic, by numerical simulation. Then, the chaotic characteristic of the system is proved by investigating the existence of a topological horseshoe in it, based on the topological horseshoe theory. At last, an electronic circuit is designed to implement the chaotic system. The results of circuit experiment coincided well with those of numerical simulation.

Generation of a New Three Dimension Autonomous Chaotic Attractor and its Four Wing Type

“…In 2011, Wang et al investigated a four-wing chaotic attractor and demonstrated that there existed heteroclinic orbits [12]. The four-wing chaotic attractors in [11,12] all meet the four-wing standards proposed in [10].…”

“…In 1976, Rossler conducted important work that rekindled the interest in three-dimensional (3D) dissipative dynamical systems [5]. Then, many Lorenz-like or Lorenzbased chaotic systems were proposed and investigated [6][7][8][9][10][11][12][13][14][15][16][17].…”

“…The authors pointed out the quadratic terms are very important in creating a four-wing chaotic attractor [10]. In 2010, Jia et al reported a four-wing chaotic attractor and the chaotic characteristic of the system was proved by investigating the existence of a topological horseshoe in it, based on the topological horseshoe theory [11]. In 2011, Wang et al investigated a four-wing chaotic attractor and demonstrated that there existed heteroclinic orbits [12].…”

Topological Horseshoe Analysis and FPGA Implementation of the Fractional-order Liu System

“…Furthermore, the topological horseshoe lemma was proposed as a practical and useful computer-assisted proof method [16]. This theory has already been used to prove the existence of chaos in some integer-order systems, for example Dong et al proved its existence in typical 3D systems [17][18][19][20], Wang et al proved the chaos existence in hyperchaos system [21][22][23][24], Jia et al analyzed the existence of chaos in fractional order Lü chaotic systems [25][26][27][28].…”

Dynamic analysis of a chaotic system

“…Latterly, by using several simple results on topological horseshoes, Li presented a new method for seeking horseshoes in dynamical systems [19]. This method has been applied to some practical systems to verify the existence of chaos [12,20,21].…”