Dynamical analysis of a new multistable chaotic system with hidden attractor: Antimonotonicity, coexisting multiple attractors, and offset boosting

2019 ◽  
Vol 383 (13) ◽  
pp. 1450-1456 ◽  
Author(s):  
Atiyeh Bayani ◽  
Karthikeyan Rajagopal ◽  
Abdul Jalil M. Khalaf ◽  
Sajad Jafari ◽  
G.D. Leutcho ◽  
...  
Keyword(s):  
Chaotic System ◽  
Dynamical Analysis ◽  
Hidden Attractor ◽  
Multiple Attractors ◽  
Offset Boosting

scholarly journals Multistability Analysis, Coexisting Multiple Attractors, and FPGA Implementation of Yu–Wang Four-Wing Chaotic System

2020 ◽  
Vol 2020 ◽  
pp. 1-16 ◽  
Author(s):  
Fei Yu ◽  
Li Liu ◽  
Hui Shen ◽  
Zinan Zhang ◽  
Yuanyuan Huang ◽  
...  
Keyword(s):  
Chaotic System ◽  
Basin Of Attraction ◽  
Fpga Implementation ◽  
Chaotic Oscillator ◽  
Stable Node ◽  
Multiple Attractors ◽  
Standard Format ◽  
Offset Boosting ◽  
The Stability ◽  
Lyapunov Exponent Spectrum

In this paper, we further study the dynamic characteristics of the Yu–Wang chaotic system obtained by Yu and Wang in 2012. The system can show a four-wing chaotic attractor in any direction, including all 3D spaces and 2D planes. For this reason, our interest is focused on multistability generation and chaotic FPGA implementation. The stability analysis, bifurcation diagram, basin of attraction, and Lyapunov exponent spectrum are given as the methods to analyze the dynamic behavior of this system. The analyses show that each system parameter has different coexistence phenomena including coexisting chaotic, coexisting stable node, and coexisting limit cycle. Some remarkable features of the system are that it can generate transient one-wing chaos, transient two-wing chaos, and offset boosting. These phenomena have not been found in previous studies of the Yu–Wang chaotic system, so they are worth sharing. Then, the RK4 algorithm of the Verilog 32-bit floating-point standard format is used to realize the autonomous multistable 4D Yu–Wang chaotic system on FPGA, so that it can be applied in embedded engineering based on chaos. Experiments show that the maximum operating frequency of the Yu–Wang chaotic oscillator designed based on FPGA is 161.212 MHz.

Dynamical analysis and passive control of a new 4D chaotic system with multiple attractors

2018 ◽  
Vol 32 (22) ◽  
pp. 1850260 ◽  
Author(s):  
Long Wang ◽  
Mei Ding
Keyword(s):  
Chaotic System ◽  
Passive Control ◽  
Strange Attractors ◽  
Dynamical Analysis ◽  
Bifurcation Diagrams ◽  
Multiple Attractors ◽  
Initial Values ◽  
System A ◽  
Periodic Attractors ◽  
Theoretical Results

This paper constructs a new 4D chaotic system from the Sprott B system. The system is dissipative, chaotic with two saddle foci. The bifurcation diagrams verify that the system exists multiple attractors with different initial values, including two strange attractors, two periodic attractors. Furthermore, we apply the passive control to control the system. A controller is designed for driving the system to the origin. The simulations show our theoretical results visually.

scholarly journals Dynamical analysis of a new chaotic system and its chaotic control

2007 ◽  
Vol 56 (11) ◽  
pp. 6230
Author(s):  
Cai Guo-Liang ◽  
Tan Zhen-Mei ◽  
Zhou Wei-Huai ◽  
Tu Wen-Tao
Keyword(s):  
Chaotic System ◽  
Dynamical Analysis ◽  
Chaotic Control ◽  
New Chaotic System

scholarly journals A Hidden Chaotic System with Multiple Attractors

Entropy ◽  
2021 ◽  
Vol 23 (10) ◽  
pp. 1341
Author(s):  
Xiefu Zhang ◽  
Zean Tian ◽  
Jian Li ◽  
Xianming Wu ◽  
Zhongwei Cui
Keyword(s):  
Phase Diagram ◽  
Lyapunov Exponent ◽  
Numerical Methods ◽  
Chaotic System ◽  
Time Domain ◽  
Chaotic Attractor ◽  
Largest Lyapunov Exponent ◽  
Spectral Entropy ◽  
Multiple Attractors ◽  
System Parameters

This paper reports a hidden chaotic system without equilibrium point. The proposed system is studied by the software of MATLAB R2018 through several numerical methods, including Largest Lyapunov exponent, bifurcation diagram, phase diagram, Poincaré map, time-domain waveform, attractive basin and Spectral Entropy. Seven types of attractors are found through altering the system parameters and some interesting characteristics such as coexistence attractors, controllability of chaotic attractor, hyperchaotic behavior and transition behavior are observed. Particularly, the Spectral Entropy algorithm is used to analyze the system and based on the normalized values of Spectral Entropy, the state of the studied system can be identified. Furthermore, the system has been implemented physically to verify the realizability.

Sign in / Sign up

Export Citation Format

Share Document