A new 4D four-wing hyperchaotic attractor and its circuit implementation

Abstract

In this paper, a new simple four-dimensional continuous-time autonomous hyperchaotic system is introduced, which displays a complicated four-wing attractor. The existence of the hyperchaos is verified by bifurcation analysis, and in the meantime bifurcation routes from period to quasi-period, then to chaos and finally to hyperchaos is determined. Different configurations of the hyperchaotic attractor are illustrated not only by computer simulation but also by electronic circuit realization. 1. INTR ODUCT I O N H yperchaos was first reported by Rossler in 1979 [1]. Since then, it has been studied with increasing interests due to its plentiful applications in applied mathematics and physics, especially in engineering and technology such as chaos-based encryption [2], secure communications [3], lasers [4], Colpitts oscillators [5], biological networks [6], nonlinear circuits [7], coupled map lattices [8], chaos control [9-1 0] and chaos synchronization [11-1 2]. The generation of different hyperchaotic systems has attracted more and more attention in the last few years [1 3 -23]. However, it is now known that generating a hyperchaotic attractor from an originally chaotic but not hyperchaotic system by means of control is a theoretically attractive and yet technically challenging task [1 7]. Some effective methods have been developed, e.g., by adding a simple state-feedback controller [1 7-18] or sinusoidal parametric perturbations [19][20], to some typical chaotic systems, which include the generalized Lorenz systems, Lorenz system, Chen system, Lu system, and a unified chaotic system to generate hyperchaotic attractor [1 7-23].Chaos attractor with four-wing has been introduced in [24-27], however, to the best of our knowledge, there are no reports on four-wing hyperchaotic attractor. In this letter, a simple and yet interesting four-dimensional (4D) continuous-time autonomous hyperchaotic system, with a complicated four-wing attractor, is firstly introduced and analyzed. "T aishan Scholarship" Construction Engineering . bifurcation analysis. Bifurcation routes: from period to quasi-period, then to chaos, and finally to hyperchaos are determined. The new-proposed system is implemented via an electronic circuit in laboratory, which shows perfect agreement with the numerical simulations. II. T HE NEW HYP ER CHA OT I C SY ST EMConsider the following 4D continuous-time autonomous system:where a,b,c,d,k,m E R+ are constant parameters.For system (1 ), one has (1 ) ax ay ai aw VV =-+-+-+-= a-b-c< °(2) ax ay az awHence, for all b + C > a , the system is dissipative. The equilibrium of system (1 ) can be found by letting the right-hand side of (1 ) be equal to zero. Obviously, the system has only one equilibrium point So = (0,0,0,0) .By linearizing system (1 ) at So = (0,0,0,0) , one obtains the Jacobian

Combinatorial synchronization of complex multiple networks with unknown parameters

“…In this paper, for convenience, we only take two different types of four-wing chaotic systems as the local node dynamics for different star-like sub-networks, which are proposed by Yu et al in [34] and Li et al in [35], respectively. The Yu system can be described as follows…”

Globally exponential synchronization of 4D four-wing hyperchaotic systems

“…The 4D four-wing hyperchaotic system [27] is described by the following nonlinear differential equations (8) is hyperchaotic [27]. The phase portrait of 4D four-wing hyperchaotic attractor of the system is given in Fig.1, when a=4, b=12, c=5.5, d=1, m=1and n=2.5.…”