scholarly journals Dynamic Analysis and Degenerate Hopf Bifurcation-Based Feedback Control of a Conservative Chaotic System and Its Circuit Simulation

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Xiaojuan Zhang ◽  
Mingshu Chen ◽  
Yang Wang ◽  
Huaigu Tian ◽  
Zhen Wang
Keyword(s):  
Numerical Simulation ◽  
Hopf Bifurcation ◽  
Feedback Control ◽  
Chaotic System ◽  
Analog Circuit ◽  
Simulation Analysis ◽  
Circuit Simulation ◽  
State Feedback Control ◽  
Stable Domain ◽  
Simulation Results

A novel conservative chaotic system with no equilibrium is investigated in this study. Various dynamics such as the conservativeness, coexistence, symmetry, and invariance are presented. Furthermore, a partial-state feedback control scheme is proposed, and the stable domain of control parameters is analyzed based on the degenerate Hopf bifurcation. In order to verify the numerical simulation analysis, an analog circuit is designed. The simulation results show that the output of the analog circuit system can reproduce the numerical simulation results and verify the correctness of the theoretical analysis.

scholarly journals A New 4D Chaotic System with Two-Wing, Four-Wing, and Coexisting Attractors and Its Circuit Simulation

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Lilian Huang ◽  
Zefeng Zhang ◽  
Jianhong Xiang ◽  
Shiming Wang
Keyword(s):  
Numerical Simulation ◽  
Chaotic System ◽  
Dynamic Characteristics ◽  
Simulation Analysis ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Coexisting Attractors ◽  
System A ◽  
Simulation Results ◽  
New System

In order to further improve the complexity of chaotic system, a new four-dimensional chaotic system is constructed based on Sprott B chaotic system. By analyzing the system’s phase diagrams, symmetry, equilibrium points, and Lyapunov exponents, it is found that the system can generate not only both two-wing and four-wing attractors but also the attractors with symmetrical coexistence, and the dynamic characteristics of the new system constructed are more abundant. In addition, the system is simulated by Multisim software, and the simulation results show that the results of circuit simulation and numerical simulation analysis are basically the same.

Output Regulation of the Liu Chaotic System

2011 ◽  
Vol 110-116 ◽  
pp. 3982-3989 ◽  
Author(s):  
Vaidyanathan Sundarapandian
Keyword(s):  
Feedback Control ◽  
Control Systems ◽  
Chaotic System ◽  
State Feedback ◽  
Output Regulation ◽  
State Feedback Control ◽  
Nonlinear Control Systems ◽  
Control Laws ◽  
Reference Signals ◽  
Simulation Results

This paper investigates the problem of regulating the output of the Liu chaotic system (2004). Explicitly, we construct state feedback control laws to regulate the Liu chaotic system so as to track constant reference signals. The control laws are derived using the regulator equations of Byrnes and Isidori (1990), who have solved the output regulation of nonlinear control systems using neutrally stable exosystem dynamics. The simulation results are also discussed in detail.

scholarly journals Low Model Analysis and Synchronous Simulation of the Wave Mechanics

2016 ◽  
Vol 2016 ◽  
pp. 1-13
Author(s):  
Wenyuan Duan ◽  
Heyuan Wang ◽  
Meng Kan
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Function ◽  
Chaotic System ◽  
Invariant Set ◽  
Positive Definite ◽  
Chaotic Attractors ◽  
Wave Mechanics ◽  
Wave Dynamics ◽  
Simulation Results ◽  
Positive Invariant Set

The dynamic behavior of a chaotic system in the internal wave dynamics and the problem of the tracing and synchronization are investigated, and the numerical simulation is carried out in this paper. The globally exponentially attractive set and positive invariant set of the chaotic system are studied via constructing the positive definite and radial unbounded Lyapunov function. There are no equilibrium positions, periodic solutions, quasi-period motions, wandering recovering motions, and other chaotic attractors of the system out of the globally exponentially attractive set. Strange attractors can only locate in the globally exponentially attractive set. A feedback controller is designed for the chaotic system to realize the control of the unstable point. The second method of Lyapunov is used to discuss theoretically the rationality of the design of the controller. The driving-response synchronization method is used to realize the globally exponential synchronization. The numerical simulation is carried out by MATLAB software, and the simulation results show that the method is effective.

scholarly journals Hopf Bifurcation and Chaos of a Delayed Finance System

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Xuebing Zhang ◽  
Honglan Zhu
Keyword(s):  
Numerical Simulation ◽  
Hopf Bifurcation ◽  
Center Manifold ◽  
Chaotic State ◽  
Bifurcation And Chaos ◽  
Finance System ◽  
Center Manifold Theorem ◽  
Normal Form Method ◽  
Simulation Results ◽  
The Stability

In this paper, a finance system with delay is considered. By analyzing the corresponding characteristic equations, the local stability of equilibrium is established. The existence of Hopf bifurcations at the equilibrium is also discussed. Furthermore, formulas for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by applying the normal form method and center manifold theorem. Finally, numerical simulation results are presented to validate the theoretical analysis. Numerical simulation results show that delay can lead a stable system into a chaotic state.

scholarly journals Generation of 3-D Grid Multi-Scroll Chaotic Attractors Based on Sign Function and Sine Function

Electronics ◽  
2020 ◽  
Vol 9 (12) ◽  
pp. 2145
Author(s):  
Pengfei Ding ◽  
Xiaoyi Feng ◽  
Lin Fa
Keyword(s):  
Chaotic System ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Time Shift ◽  
Chaotic Attractors ◽  
Sine Function ◽  
Sign Function ◽  
Simulation Results ◽  
Jerk System ◽  
Lyapunov Exponent Spectrum

A three directional (3-D) multi-scroll chaotic attractors based on the Jerk system with nonlinearity of the sine function and sign function is introduced in this paper. The scrolls in the X-direction are generated by the sine function, which is a modified sine function (MSF). In addition, the scrolls in Y and Z directions are generated by the sign function series, which are the superposition of some sign functions with different time-shift values. In the X-direction, the scroll number is adjusted by changing the comparative voltages of the MSF, and the ones in Y and Z directions are regulated by the sign function. The basic dynamics of Lyapunov exponent spectrum, phase diagrams, bifurcation diagram and equilibrium points distribution were studied. Furthermore, the circuits of the chaotic system are designed by Multisim10, and the circuit simulation results indicate the feasibility of the proposed chaotic system for generating chaotic attractors. On the basis of the circuit simulations, the hardware circuits of the system are designed for experimental verification. The experimental results match with the circuit simulation results, this powerfully proves the correctness and feasibility of the proposed system for generating 3-D grid multi-scroll chaotic attractors.

The Effects of a Constant Excitation Force on the Dynamics of an Infinite-Equilibrium Chaotic System Without Linear Terms: Analysis, Control and Circuit Simulation

2020 ◽  
Vol 30 (15) ◽  
pp. 2050234
Author(s):  
L. Kamdjeu Kengne ◽  
Z. Tabekoueng Njitacke ◽  
J. R. Mboupda Pone ◽  
H. T. Kamdem Tagne
Keyword(s):  
Chaotic System ◽  
Analog Circuit ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Nonlinear Behavior ◽  
Basins Of Attraction ◽  
Phase Portraits ◽  
Unique Contribution ◽  
Chaotic Signals ◽  
Excitation Force

In this paper, the effects of a bias term modeling a constant excitation force on the dynamics of an infinite-equilibrium chaotic system without linear terms are investigated. As a result, it is found that the bias term reduces the number of equilibrium points (transition from infinite-equilibria to only two equilibria) and breaks the symmetry of the model. The nonlinear behavior of the system is highlighted in terms of bifurcation diagrams, maximal Lyapunov exponent plots, phase portraits, and basins of attraction. Some interesting phenomena are found including, for instance, hysteretic dynamics, multistability, and coexisting bifurcation branches when monitoring the system parameters and the bias term. Also, we demonstrate that it is possible to control the offset and amplitude of the chaotic signals generated. Compared to some few cases previously reported on systems without linear terms, the plethora of behaviors found in this work represents a unique contribution in comparison with such type of systems. A suitable analog circuit is designed and used to support the theoretical analysis via a series of Pspice simulations.

Six-Dimensional Chaotic System and its Circuit Implementation

2011 ◽  
Vol 255-260 ◽  
pp. 2018-2022 ◽  
Author(s):  
Jian Liang Zhu ◽  
Yu Jing Wang ◽  
Shou Qiang Kang
Keyword(s):  
Numerical Simulation ◽  
Power Spectrum ◽  
Chaotic System ◽  
Time Domain ◽  
Circuit Simulation ◽  
System Simulation ◽  
Practical Significance ◽  
Chaotic Attractors ◽  
Circuit Implementation ◽  
Product Term

In order to generate complex chaotic attractors, a six-dimensional chaotic system is designed, which contains six parameters and each equation contains a nonlinear product term. When its parameters satisfy certain conditions, the system is chaotic. By Matlab numerical simulation, chaotic attractor and relevant Lyapunov exponents spectrum can be obtained, which validates that the system is chaotic. And, time domain waveform and power spectrum are shown. Finally, the implementation circuit of this system is designed, and circuit simulation can be done by using Multisim. Circuit simulation result is identical to system simulation completely. The circuit has a practical significance in secrecy communication and correlative fields.

A New Five Dimensional Hyperchaotic System and its Fractional Order Form

2013 ◽  
Vol 464 ◽  
pp. 375-380 ◽  
Author(s):  
Ling Liu ◽  
Chong Xin Liu ◽  
Yi Fan Liao
Keyword(s):  
Numerical Simulation ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Simulation Analysis ◽  
Three Dimensional ◽  
Hyperchaotic System ◽  
Order Form ◽  
Simulation Results ◽  
Predictor Corrector ◽  
New Hyperchaotic System

In this paper, a new five-dimensional hyperchaotic system by introducing two additional states feedback into a three-dimensional smooth chaotic system. With three nonlinearities, this system has more than one positive Lyapunov exponents. Based on the fractional derivative theory, the fractional-order form of this new hyperchaotic system has been investigated. Through predictor-corrector algorithm, the system is proved by numerical simulation analysis. Simulation results are provided to illustrate the performance of the fractional-order hyperchaotic attractors well.

Numerical Simulation Analysis on Explosion Stress Field of Different Charge Construction

2011 ◽  
Vol 250-253 ◽  
pp. 2612-2616 ◽  
Author(s):  
Qi Zong ◽  
Lu Ping Yan ◽  
Hai Bo Wang
Keyword(s):  
Numerical Simulation ◽  
Stress Field ◽  
Simulation Analysis ◽  
Blast Hole ◽  
Peak Stress ◽  
Wall Pressure ◽  
Energy Utilization ◽  
Good Energy ◽  
Maximum Water ◽  
Simulation Results

There are different blasting stress field which around the blast hole caused by different charge when explosives exploded in the rock. Simulation analysis on borehole wall pressure and explosion stress field of rock at different charging structure was done by ANSYS/LS-DYNA. The simulation results indicate: stress of coupling charge is the maximum, water-decouple charge is the latter and air-decouple charge is the minimum; and whether air-decouple or water-decouple charge, peak stress value of model decreased along with the increasing of decouple coefficient, but the air-decouple charge show more obvious. Therefore, water-decouple blasting has good energy utilization.

scholarly journals Numerical Simulation Analysis of Cavitation Performance of Tandem Propeller

2018 ◽  
Vol 36 (3) ◽  
pp. 509-515 ◽  
Author(s):  
Xiaoxu Du ◽  
Zhengdong Zhang
Keyword(s):  
Numerical Simulation ◽  
Simulation Analysis ◽  
Cavitation Number ◽  
Hydrodynamic Characteristics ◽  
Turbulent Model ◽  
Cavitation Model ◽  
Cavitation Phenomenon ◽  
Cavitation Performance ◽  
Simulation Results ◽  
Good Agreement

The steady non cavitation hydrodynamic characteristics of CLB4-55-1 tandem propeller and the steady cavitation flows of NACA66 hydrofoil are numerically studied firstly based on the RANS equations of homogeneous multiphase using CFD theory, combined with the SST k-ω turbulent model and Z-G-B cavitation model. Numerical simulation results are in good agreement with the experimental results, which indicates that the numerical method is reliable and accurate. Then, the cavitation performance of the tandem propeller are numerical simulated and analyzed. The results show that the computational model can predict the cavitation performance of tandem propeller accurately. The cavitation performance of tandem propeller is nearly the same as single propeller, however, the cavitation phenomenon of back propeller is greater than the head propeller at certain advance coefficient and cavitation number. The cavitation phenomenon will disappear with the increase of the advance coefficient or the cavitation number.

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