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.

Dynamic analysis, FPGA implementation, and cryptographic application of an autonomous 5D chaotic system with offset boosting

2020 ◽  
Vol 21 (6) ◽  
pp. 950-961
Author(s):  
Sifeu Takougang Kingni ◽  
Karthikeyan Rajagopal ◽  
Serdar Çiçek ◽  
Ashokkumar Srinivasan ◽  
Anitha Karthikeyan
Keyword(s):  
Dynamic Analysis ◽  
Chaotic System ◽  
Fpga Implementation ◽  
Offset Boosting

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 CCII and FPGA Realization: A Multistable Modified Fourth-Order Autonomous Chua’s Chaotic System with Coexisting Multiple Attractors

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-17 ◽  
Author(s):  
Fei Yu ◽  
Hui Shen ◽  
Li Liu ◽  
Zinan Zhang ◽  
Yuanyuan Huang ◽  
...  
Keyword(s):  
Limit Cycle ◽  
Chaotic System ◽  
Fourth Order ◽  
Secure Communication ◽  
Random Number Generator ◽  
Cycle Period ◽  
Chaotic Oscillator ◽  
Current Conveyors ◽  
Multiple Attractors ◽  
Operation Speed

In this paper, a multistable modified fourth-order autonomous Chua’s chaotic system is investigated. In addition to the dynamic characteristics of the third-order Chua’s chaotic system itself, what interests us is that this modified fourth-order autonomous Chua’s chaotic system has five different types of coexisting attractors: double-scroll, single band chaotic attractor, period-4 limit cycle, period-2 limit cycle, and period-1 limit cycle. Then, an inductorless modified fourth-order autonomous Chua’s chaotic circuit is proposed. The active elements as well as the synthetic inductor employed in this circuit are designed using second-generation current conveyors (CCIIs). The reason for using CCIIs is that they have high conversion rate and operation speed, which enable the circuit to work at a higher frequency range. The Multisim simulations confirm the theoretical estimates of the performance of the proposed circuit. Finally, using RK-4 numerical algorithm of VHDL 32-bit IQ-Math floating-point number format, the inductorless modified fourth-order autonomous Chua’s chaotic system is implemented on FPGA for the development of embedded engineering applications based on chaos. The system is simulated and synthesized on Virtex-6 FPGA chip. The maximum operating frequency of modified Chua’s chaotic oscillator based on FPGA is 180.180 MHz. This study demonstrates that the hardware-based multistable modified fourth-order autonomous Chua’s chaotic system is a very good source of entropy and can be applied to various embedded systems based on chaos, including secure communication, cryptography, and random number generator.

scholarly journals On the Stability and Multistability in a Duopoly Game with R&D Spillover and Price Competition

2019 ◽  
Vol 2019 ◽  
pp. 1-20 ◽  
Author(s):  
Wei Zhou ◽  
Xiao-Xue Wang
Keyword(s):  
Price Competition ◽  
Equilibrium Points ◽  
Research Result ◽  
Basin Of Attraction ◽  
Profit Maximization ◽  
Feasible Region ◽  
Multiple Attractors ◽  
Critical Curves ◽  
Coexistence Of Multiple Attractors ◽  
The Stability

In this paper, a dynamical two-stage game with R&D competition and joint profit maximization is built. The stability of all the equilibrium points is discussed through Jury condition, and the stability region of the Nash equilibrium point is then given. The influence of the parameters on the system is discussed, and we find that the firm can even benefit from chaos, when it has higher innovation efficiency and higher adjusting speed. And then the coexistence of multiple attractors is studied using basin of attraction. Our research result shows that the coexisting attractors can be observed in the two-parameter bifurcation diagram. At last, the boundary of feasible region, global bifurcations, and formation mechanism of fractal structure of attracting basin are analyzed through critical curves and noninvertible map theory.

scholarly journals Sliding Mode Control and Modified Generalized Projective Synchronization of a New Fractional-Order Chaotic System

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Junbiao Guan ◽  
Kaihua Wang
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Secure Communication ◽  
Sliding Mode ◽  
Projective Synchronization ◽  
Control Technique ◽  
Order System ◽  
Mode Control ◽  
The Stability

A new fractional-order chaotic system is addressed in this paper. By applying the continuous frequency distribution theory, the indirect Lyapunov stability of this system is investigated based on sliding mode control technique. The adaptive laws are designed to guarantee the stability of the system with the uncertainty and external disturbance. Moreover, the modified generalized projection synchronization (MGPS) of the fractional-order chaotic systems is discussed based on the stability theory of fractional-order system, which may provide potential applications in secure communication. Finally, some numerical simulations are presented to show the effectiveness of the theoretical results.

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.

scholarly journals Theory and applications of new fractional-order chaotic system under Caputo operator

2021 ◽  
Vol 12 (1) ◽  
pp. 20-38
Author(s):  
Ndolane Sene
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Caputo Derivative ◽  
Phase Portraits ◽  
Chaotic Circuit ◽  
Chaotic Model ◽  
The Stability ◽  
The Impact ◽  
Schematic Circuit ◽  
Good Agreement

This paper introduces the properties of a fractional-order chaotic system described by the Caputo derivative. The impact of the fractional-order derivative has been focused on. The phase portraits in different orders are obtained with the aids of the proposed numerical discretization, including the discretization of the Riemann-Liouville fractional integral. The stability analysis has been used to help us to delimit the chaotic region. In other words, the region where the order of the Caputo derivative involves and where the presented system in this paper is chaotic. The nature of the chaos has been established using the Lyapunov exponents in the fractional context. The schematic circuit of the proposed fractional-order chaotic system has been presented and simulated in via Mutltisim. The results obtained via Multisim simulation of the chaotic circuit are in good agreement with the results with Matlab simulations. That provided the fractional operators can be applied in real- worlds applications as modeling electrical circuits. The presence of coexisting attractors for particular values of the parameters of the presented fractional-order chaotic model has been studied.

Sign in / Sign up

Export Citation Format

Share Document