The novel control method of three dimensional discrete hyperchaotic Hénon map

2014 ◽  
Vol 247 ◽  
pp. 487-493 ◽  
Author(s):  
Shao-Fu Wang ◽  
Xiao-Cong Li ◽  
Fei Xia ◽  
Zhan-Shan Xie
Keyword(s):  
Control Method ◽  
Three Dimensional ◽  
The Novel ◽  
Hénon Map ◽  
Henon Map

scholarly journals Detecting and stabilizing periodic orbits of chaotic Henon map through predictive control

2018 ◽  
Vol 27 (2018) ◽  
pp. 73-78
Author(s):  
Dumitru Deleanu
Keyword(s):  
Periodic Orbits ◽  
Predictive Control ◽  
Nonnegative Integer ◽  
Strange Attractor ◽  
Discrete System ◽  
Control Method ◽  
Nonlinear Mapping ◽  
Unstable Periodic Orbits ◽  
Hénon Map ◽  
Henon Map

The predictive control method is one of the proposed techniques based on the location and stabilization of the unstable periodic orbits (UPOs) embedded in the strange attractor of a nonlinear mapping. It assumes the addition of a small control term to the uncontrolled state of the discrete system. This term depends on the predictive state ps + 1 and p(s + 1) + 1 iterations forward, where s is the length of the UPO, and p is a large enough nonnegative integer. In this paper, extensive numerical simulations on the Henon map are carried out to confirm the ability of the predictive control to detect and stabilize all the UPOs up to a maximum length of the period. The role played by each involved parameter is investigated and additional results to those reported in the literature are presented.

scholarly journals Climbing and Turning Control of a Biped Passive Walker by Periodic Input Based on Frequency Entrainment

2011 ◽  
Vol 2-3 ◽  
pp. 48-52 ◽  
Author(s):  
Soichiro Suzuki ◽  
Ying Cao ◽  
Masamichi Takada ◽  
Kentaro Oi
Keyword(s):  
Control Method ◽  
Three Dimensional ◽  
Frontal Plane ◽  
The Novel ◽  
Mechanical Oscillator ◽  
Frequency Entrainment ◽  
Periodic Input ◽  
Target Path ◽  
Turning Control

This study is aimed at stabilizing a three dimensional biped passive walker in various environments and achieving climbing and turning control. The novel control method synchronizes a period of the changing motion of the stance leg in frontal plane (frontal motion) with a period of the swing leg by periodic input in order to stabilize the three dimensional passive walker. A mechanical oscillator is utilized to change the period of the frontal motion. The target path of the oscillator is automatically generated based on frequency entrainment in order to adjust the period of the frontal motion. In the climbing and turning control of the passive walker, the amplitude and the phase generating algorithm of the target path of the oscillator are improved. It is analytically demonstrated that the biped passive walker can be stabilized even in climbing and turning.

scholarly journals Bifurcation analysis of the three-dimensional Hénon map

2017 ◽  
Vol 10 (3) ◽  
pp. 625-645 ◽  
Author(s):  
Ming Zhao ◽  
◽  
Cuiping Li ◽  
Jinliang Wang ◽  
Zhaosheng Feng ◽  
...  
Keyword(s):  
Bifurcation Analysis ◽  
Three Dimensional ◽  
Hénon Map ◽  
Henon Map

THREE-DIMENSIONAL HÉNON-LIKE MAPS AND WILD LORENZ-LIKE ATTRACTORS

2005 ◽  
Vol 15 (11) ◽  
pp. 3493-3508 ◽  
Author(s):  
S. V. GONCHENKO ◽  
I. I. OVSYANNIKOV ◽  
C. SIMÓ ◽  
D. TURAEV
Keyword(s):  
Lyapunov Exponent ◽  
Parameter Space ◽  
Chaotic Dynamics ◽  
Three Dimensional ◽  
Maximal Lyapunov Exponent ◽  
Hénon Map ◽  
Henon Map ◽  
Quadratic Map ◽  
Different Types ◽  
Natural Way

We discuss a rather new phenomenon in chaotic dynamics connected with the fact that some three-dimensional diffeomorphisms can possess wild Lorenz-type strange attractors. These attractors persist for open domains in the parameter space. In particular, we report on the existence of such domains for a three-dimensional Hénon map (a simple quadratic map with a constant Jacobian which occurs in a natural way in unfoldings of several types of homoclinic bifurcations). Among other observations, we have evidence that there are different types of Lorenz-like attractor domains in the parameter space of the 3D Hénon map. In all cases the maximal Lyapunov exponent, Λ1, is positive. Concerning the next Lyapunov exponent, Λ2, there are open domains where it is definitely positive, others where it is definitely negative and, finally, domains where it cannot be distinguished numerically from zero (i.e. |Λ2| < ρ, where ρ is some tolerance ranging between 10-5 and 10-6). Furthermore, several other types of interesting attractors have been found in this family of 3D Hénon maps.

scholarly journals Bifurcations and chaos in a three-dimensional generalized Hénon map

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Jingjing Zheng ◽  
Ziwei Wang ◽  
You Li ◽  
Jinliang Wang
Keyword(s):  
Three Dimensional ◽  
Hénon Map ◽  
Henon Map ◽  
Generalized Hénon Map

Stabilization and circuit implementation of a novel chemical oscillating chaotic system

Circuit World ◽  
2019 ◽  
Vol 45 (2) ◽  
pp. 93-106
Author(s):  
Li Xiong ◽  
Wanjun Yin ◽  
Xinguo Zhang
Keyword(s):  
Chaotic System ◽  
Control Method ◽  
Three Dimensional ◽  
Chaotic Attractors ◽  
The Novel ◽  
Content Type ◽  
Initial Values ◽  
Parameters Selection ◽  
Chaotic Circuits ◽  
Simulation Results

Purpose This paper is aimed at investigating a novel chemical oscillating chaotic system with different attractors at fixed parameters. The typical dynamical behavior of the new chemical oscillating system is discussed, and it is found that the state selection is dependent on initial values. Then, the stabilization problem of the chemical oscillating attractors is investigated analytically and numerically. Subsequently, the novel electronic circuit of the proposed chemical oscillating chaotic system are constructed, and the influences of the changes of circuit parameters on chemical oscillating chaotic attractors are investigated. Design/methodology/approach The different attractors of the novel chemical oscillating chaotic system are investigated by changing the initial values under fixed parameters. Moreover, the active control and adaptive control methods are presented to make the chemical oscillating chaotic systems asymptotically stable at the origin based on the Lyapunov stability theory. The influences on chemical oscillating chaotic attractors are also verified by changing the circuit parameters. Findings It is found that the active control method is easier to be realized by using physical components because of its less control signal and lower cost. It is also confirmed that the adaptive control method enjoys strong anti-interference ability because of its large number of selected controllers. What can be seen from the simulation results is that the chaotic circuits are extremely dependent on circuit parameters selection. Comparisons between MATLAB simulations and Multisim simulation results show that they are consistent with each other and demonstrate that changing attractors of the chemical oscillating chaotic system exist. It is conformed that circuit parameters selection can be effective to control and realize chaotic circuits. Originality/value The different attractors of the novel chemical oscillating chaotic system are investigated by changing the initial values under fixed parameters. The characteristic of the chemical oscillating attractor is that the basin of attraction of the three-dimensional attractor is located in the first quadrant of the eight quadrants of the three-dimensional space, and the ranges of the three variables are positive. This is because the concentrations of the three chemical substances are all positive.

scholarly journals The fractional form of a new three-dimensional generalized Hénon map

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Lotfi Jouini ◽  
Adel Ouannas ◽  
Amina-Aicha Khennaoui ◽  
Xiong Wang ◽  
Giuseppe Grassi ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Hénon Map ◽  
Henon Map ◽  
Generalized Hénon Map

Numerical Study of a Three-Dimensional Hénon Map

2011 ◽  
Vol 28 (1) ◽  
pp. 010203 ◽  
Author(s):  
Gabriela A Casas ◽  
Paulo C Rech
Keyword(s):  
Numerical Study ◽  
Three Dimensional ◽  
Hénon Map ◽  
Henon Map

On the Three-Dimensional Fractional-Order Hénon Map with Lorenz-Like Attractors

2020 ◽  
Vol 30 (11) ◽  
pp. 2050217
Author(s):  
Amina-Aicha Khennaoui ◽  
Adel Ouannas ◽  
Zaid Odibat ◽  
Viet-Thanh Pham ◽  
Giuseppe Grassi
Keyword(s):  
Fractional Order ◽  
Chaotic Map ◽  
Three Dimensional ◽  
Synchronization Control ◽  
Fractional Order Systems ◽  
Bifurcation Diagrams ◽  
Hénon Map ◽  
Henon Map ◽  
Control Scheme ◽  
Fractional Orders

A three-dimensional (3D) Hénon map of fractional order is proposed in this paper. The dynamics of the suggested map are numerically illustrated for different fractional orders using phase plots and bifurcation diagrams. Lorenz-like attractors for the considered map are realized. Then, using the linear fractional-order systems stability criterion, a controller is proposed to globally stabilize the fractional-order Hénon map. Furthermore, synchronization control scheme has been designed to exhibit a synchronization behavior between a given 2D fractional-order chaotic map and the 3D fractional-order Hénon map. Numerical simulations are also performed to verify the main results of the study.

Disorganization of a hole tone feedback loop by an axisymmetric obstacle on a downstream end plate

2014 ◽  
Vol 757 ◽  
pp. 908-942 ◽  
Author(s):  
K. Matsuura ◽  
M. Nakano
Keyword(s):  
Nozzle Exit ◽  
Passive Control ◽  
Control Method ◽  
Three Dimensional ◽  
Acoustic Power ◽  
Shear Layers ◽  
Mean Velocity ◽  
End Plate ◽  
Air Jet ◽  
Practical Engineering

AbstractThis study investigates the suppression of the sound produced when a jet, issued from a circular nozzle or hole in a plate, goes through a similar hole in a second plate. The sound, known as a hole tone, is encountered in many practical engineering situations. The mean velocity of the air jet $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}u_0$ was $6\text {--}12\ \mathrm{m}\ {\mathrm{s}}^{-1}$. The nozzle and the end plate hole both had a diameter of 51 mm, and the impingement length $L_{im}$ between the nozzle and the end plate was 50–90 mm. We propose a novel passive control method of suppressing the tone with an axisymmetric obstacle on the end plate. We find that the effect of the obstacle is well described by the combination ($W/L_{im}$, $h$) where $W$ is the distance from the edge of the end plate hole to the inner wall of the obstacle, and $h$ is the obstacle height. The tone is suppressed when backflows from the obstacle affect the jet shear layers near the nozzle exit. We do a direct sound computation for a typical case where the tone is successfully suppressed. Axisymmetric uniformity observed in the uncontrolled case is broken almost completely in the controlled case. The destruction is maintained by the process in which three-dimensional vortices in the jet shear layers convect downstream, interact with the obstacle and recursively disturb the jet flow from the nozzle exit. While regions near the edge of the end plate hole are responsible for producing the sound in the controlled case as well as in the uncontrolled case, acoustic power in the controlled case is much lower than in the uncontrolled case because of the disorganized state.

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