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

Abstract

In this paper, a new three-dimension (3D) autonomous chaotic system with a nonlinear term in the form of a hyperbolic sine (or cosine) function is reported. Some interesting and complex attractors are obtained. Basic dynamical properties of the new chaotic system are demonstrated in terms of Lyapunov exponents, Poincare mapping, fractal dimension and continuous spectrum. Meanwhile, for further enhancing the complexity of the topological structure of the new chaotic attractors, the attractors are changed from two-wing to four-wing through making axis doubly polarized, theoretically analyzed and numerically simulated. The obtained results clearly show that the chaotic system deserves further detailed investigation.

Zero–Hopf bifurcations in Yu–Wang type systems

“…More recently, in 2013 Yu and Wang, introduced a new three dimensional chaotic system with a complicated structure which we write here in order to have a self contained paper ẋ =a(y − x), ẏ =bx − cxz, ż = sinh(xy) − dz, (1) with a, b, c, d ∈ R. The above system has a nonpolynomial structure, considered by the authors in a previous work [15]. System (1) possesses a new strange attractor with four wings [16]. A nice analysis of the complicated structure of a four wing system appears in a e-mail: abimael.bengochea@itam.mx b e-mail: alechung@xanum.uam.mx c e-mail: ernesto.perez@itam.mx (corresponding author) [11] and also in [14].…”

“…Most of the studies of Yu-Wang systems have been carried out attending their chaotic dynamics, for example, focusing on their Lyapunov exponents, or others dynamical features [16]. In this work, we are interested in the zero Hopf-bifurcation of the Yu-Wang type system (2), that is to say, the birth of periodic orbits from an equilibrium point whose linear part has a zero eigenvalue, and a pair of purely imaginary eigenvalues.…”