5D Hyper-Chaotic System with Multiple Types of Equilibrium Points
- PDF / 1,985,677 Bytes
- 11 Pages / 612.284 x 810.709 pts Page_size
- 30 Downloads / 206 Views
5D Hyper-Chaotic System with Multiple Types of Equilibrium Points
),
XU Changbiaoa,b (
WU Xiaa∗ (
),
ï),
HE Yinghuib (
MO Yunhuia (
ï)
(a. School of Communication and Information Engineering; b. School of Optoelectronic Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China)
© Shanghai Jiao Tong University and Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract: A chaotic system with various equilibrium types has rich dynamic behaviors. Its state can switch flexibly among different families of attractors, which is beneficial to the practical applications. So it has been widely concerned in recent years. In this paper, a new 5D hyper-chaotic system is proposed. The important characteristic of the system is that it may have multiple types of equilibrium points by changing system parameters, namely, linear equilibrium point, no equilibrium point, non-hyperbolic unstable equilibrium point and stable hyperbolictype equilibrium point. Furthermore, there are hyper-chaotic phenomena and multi-stability about the coexistence of multiple chaotic attractors and the coexistence of hyper-chaotic attractors and chaotic attractors in the system. In addition, the system’s complexity is analyzed. It is found that the complexity is close to 1 in the hyper-chaotic state and a pseudo-random sequence generated by the system passes all the statistical tests. Finally, an analog circuit of the system is designed and simulated. Key words: hyper-chaos, equilibrium point, multi-stability, pseudorandom sequence, chaotic circuit CLC number: TP 273 Document code: A
0 Introduction The equilibrium point of a chaotic system plays an important role in dynamic analysis, theoretical design and amplitude modulation of attractors[1]. If all the real parts of the eigenvalues for an equilibrium point are nonzero, the equilibrium point is called hyperbolic equilibrium point[2] ; if one or more real parts of the eigenvalues for the equilibrium point are zero, it is called non-hyperbolic equilibrium point[3] . Hyperbolic equilibrium points can be stable or unstable saddle points, focal points or saddle focal points, while nonhyperbolic equilibrium points do not exist saddle-focal points[4] . The study on the property of system equilibrium point is helpful to explore the type and shape of attractors[5-6] , the amplitude variation of signal[7] and its application in practical engineering[8-10] . Leonov et al. have divided the dynamical systems into two categories: dynamical systems with self-excited attractors and dynamical systems with hidden attractors[11-13] . A basin of attraction of a self-excited attractor contains at least one unstable equilibrium point, while that of a hidden attractor does not intersect with the neighborhood of any unstable equilibrium point[14-15] . Chaotic systems with stable equilibrium points, infinite equilibReceived date: 2019-09-07 Foundation item: the Science Foundation of Ministry of Education of China (No. 02152) ∗E-mail: [email protected]
rium points and no
Data Loading...
