scholarly journals A 2D Hyperchaotic Map: Amplitude Control, Coexisting Symmetrical Attractors and Circuit Implementation

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1047
Author(s):  
Xuejiao Zhou ◽  
Chunbiao Li ◽  
Xu Lu ◽  
Tengfei Lei ◽  
Yibo Zhao
Keyword(s):  
Value Function ◽  
Initial Conditions ◽  
Opposite Polarity ◽  
Partial Amplitude ◽  
Circuit Implementation ◽  
Coexisting Attractors ◽  
Amplitude Control ◽  
Absolute Value ◽  
Numerical Exploration ◽  
Discrete Map

An absolute value function was introduced for chaos construction, where hyperchaotic oscillation was found with amplitude rescaling. The nonlinear absolute term brings the convenience for amplitude control. Two regimes of amplitude control including total and partial amplitude control are discussed, where the attractor can be rescaled separately by two independent coefficients. Symmetrical pairs of coexisting attractors are captured by corresponding initial conditions. Circuit implementation by the platform STM32 is consistent with the numerical exploration and the theoretical observation. This finding is helpful for promoting discrete map application, where amplitude control is realized in an easy way and coexisting symmetrical sequences with opposite polarity are obtained.

Controlling Coexisting Attractors of Conditional Symmetry

2019 ◽  
Vol 29 (14) ◽  
pp. 1950207 ◽  
Author(s):  
Tianai Lu ◽  
Chunbiao Li ◽  
Sajad Jafari ◽  
Fuhong Min
Keyword(s):  
Chaotic Systems ◽  
Value Function ◽  
Opposite Polarity ◽  
Conditional Symmetry ◽  
Coexisting Attractors ◽  
Absolute Value ◽  
Offset Boosting

Conditional symmetry is known as a new regime for providing coexisting duplicate oscillations with opposite polarity. Polarity balance can be obtained from a function for hosting conditional symmetry. In this paper, new cases of chaotic systems with conditional symmetry are coined from 1D and 2D offset boosting based on a suitable polarity adjustment. Conditional symmetric attractors are controlled effectively by a simple absolute value function, where the distance between two coexisting attractors of conditional symmetry is modified linearly by the offset boosting constant, meanwhile the size of the coexisting attractors gets controlled by the slope. Coexisting attractors of conditional symmetry are thereafter implemented based on the develop kit of STM32.

Hidden Attractors with Conditional Symmetry

2020 ◽  
Vol 30 (14) ◽  
pp. 2030042
Author(s):  
Chunbiao Li ◽  
Jiayu Sun ◽  
Julien Clinton Sprott ◽  
Tengfei Lei
Keyword(s):  
Numerical Simulation ◽  
Chaotic Systems ◽  
Value Function ◽  
Chaotic Attractors ◽  
Circuit Implementation ◽  
Conditional Symmetry ◽  
Hidden Attractors ◽  
Engineering Technology ◽  
Absolute Value

By introducing an absolute value function for polarity balance, some new examples of chaotic systems with conditional symmetry are constructed that have hidden attractors. Coexisting oscillations along with bifurcations are investigated by numerical simulation and circuit implementation. Such new cases enrich the gallery of hidden chaotic attractors of conditional symmetry that are potentially useful in engineering technology.

A Simple Nonautonomous Hidden Chaotic System with a Switchable Stable Node-Focus

2019 ◽  
Vol 29 (12) ◽  
pp. 1950168 ◽  
Author(s):  
Bocheng Bao ◽  
Jiaoyan Luo ◽  
Han Bao ◽  
Chengjie Chen ◽  
Huagan Wu ◽  
...  
Keyword(s):  
Phase Plane ◽  
Value Function ◽  
Analog Circuit ◽  
Nonautonomous System ◽  
Stable Node ◽  
Two Dimensional ◽  
Coexisting Attractors ◽  
Absolute Value ◽  
Dynamical Behaviors ◽  
Hidden Oscillations

This paper presents a simple two-dimensional nonautonomous system, which possesses piecewise linearity constructed by a simple absolute value function. The nonautonomous system has only one switchable equilibrium state with a stable node-focus in the considered control parameter region but can generate periodic, chaotic and coexisting attractors. Therefore, the presented simple two-dimensional nonautonomous system always operates with hidden oscillations, which is not similar to any example reported in the literature. Furthermore, specific hidden dynamical behaviors are numerically disclosed by employing one-dimensional and two-dimensional bifurcation plots, phase plane plots, Poincaré mappings, local attraction basins, and complexity plots. In addition, by utilizing the circuit module of the absolute value function, a multiplierless analog circuit is designed, based on which breadboard experiments are performed to validate the numerically simulated phase plane plots of coexisting attractors.

scholarly journals Infinitely Many Coexisting Attractors in No-Equilibrium Chaotic System

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Qiang Lai ◽  
Paul Didier Kamdem Kuate ◽  
Huiqin Pei ◽  
Hilaire Fotsin
Keyword(s):  
Adaptive Control ◽  
Chaotic System ◽  
Physical Meaning ◽  
Control Method ◽  
Initial Conditions ◽  
Periodic Motions ◽  
Hidden Attractors ◽  
Coexisting Attractors ◽  
Dynamic Behaviors

This paper proposes a new no-equilibrium chaotic system that has the ability to yield infinitely many coexisting hidden attractors. Dynamic behaviors of the system with respect to the parameters and initial conditions are numerically studied. It shows that the system has chaotic, quasiperiodic, and periodic motions for different parameters and coexists with a large number of hidden attractors for different initial conditions. The circuit and microcontroller implementations of the system are given for illustrating its physical meaning. Also, the synchronization conditions of the system are established based on the adaptive control method.

scholarly journals Composite One- to Six-Scroll Hidden Attractors in a Memristor-Based Chaotic System and Their Circuit Implementation

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Ying Li ◽  
Xiaozhu Xia ◽  
Yicheng Zeng ◽  
Qinghui Hong
Keyword(s):  
Fixed Point ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Circuit Implementation ◽  
Hidden Attractors ◽  
Coexisting Attractors ◽  
Extreme Multistability ◽  
Different Types ◽  
Hardware Circuit ◽  
New System

Chaotic systems with hidden multiscroll attractors have received much attention in recent years. However, most parts of hidden multiscroll attractors previously reported were repeated by the same type of attractor, and the composite of different types of attractors appeared rarely. In this paper, a memristor-based chaotic system, which can generate composite attractors with one up to six scrolls, is proposed. These composite attractors have different forms, similar to the Chua’s double scroll and jerk double scroll. Through theoretical analysis, we find that the new system has no fixed point; that is to say, all of the composite multiscroll attractors are hidden attractors. Additionally, some complicated dynamic behaviors including various hidden coexisting attractors, extreme multistability, and transient transition are explored. Moreover, hardware circuit using discrete components is implemented, and its experimental results supported the numerical simulations results.

scholarly journals Trapping Time of Resonant Orbits in Presence of Poynting - Robertson Drag

1983 ◽  
Vol 74 ◽  
pp. 397-410 ◽  
Author(s):  
R. Gonczi ◽  
Ch. Froeschlé ◽  
C. Froeschlé
Keyword(s):  
Initial Conditions ◽  
Gravitational Interaction ◽  
Resonance Region ◽  
Three Body Problem ◽  
Trapping Time ◽  
Resonant Orbits ◽  
Numerical Exploration ◽  
Orbital Resonances ◽  
Three Body ◽  
Special Case

AbstractWe study numerically the competition between the Poynting-Robertson drag and the gravitational interaction of grains with Jupiter near orbital resonances. The computations are based on the plane elliptic restricted three body problem. Numerical investigations show that the grains always cross the resonance region without any oscillation, except in the special case where the grains were initially inside the resonance. Such grains are temporarily trapped, then due to the drag they are ejected out of the resonance. The trapping time of a particle turns out to be much more important in the 3/2 and 2/1 commensurabilities than in the others.A numerical exploration of numerous orbits for different initial conditions and different sizes of grains has been performed. The trapping time appears to be closely connected to the size of the librator-type orbits regions; it increases with the initial eccentricity of the orbit, and is also proportional to the radius and the density of the particle.

scholarly journals Polar Metric-Weighted Norm-Based Scan Matching for Robot Pose Estimation

2016 ◽  
Vol 2016 ◽  
pp. 1-20
Author(s):  
Guanglei Huo ◽  
Lijun Zhao ◽  
Ke Wang ◽  
Ruifeng Li ◽  
Jianqiang Li
Keyword(s):  
Pose Estimation ◽  
Value Function ◽  
Rotation Angle ◽  
Accurate Estimation ◽  
Weighted Norm ◽  
Map Building ◽  
Scan Matching ◽  
Constant Weight ◽  
Absolute Value ◽  
Point To Point

A novel point-to-point scan matching approach is proposed to address pose estimation and map building issues of mobile robots. Polar Scan Matching (PSM) and Metric-Based Iterative Closest Point (Mb-ICP) are usually employed for point-to-point scan matching tasks. However, due to the facts that PSM considers the distribution similarity of polar radii in irrelevant region of reference and current scans and Mb-ICP assumes a constant weight in the norm about rotation angle, they may lead to a mismatching of the reference and current scan in real-world scenarios. In order to obtain better match results and accurate estimation of the robot pose, we introduce a new metric rule, Polar Metric-Weighted Norm (PMWN), which takes both rotation and translation into account to match the reference and current scan. For robot pose estimation, the heading rotation angle is estimated by correspondences establishing results and further corrected by an absolute-value function, and then the geometric property of PMWN called projected circle is used to estimate the robot translation. The extensive experiments are conducted to evaluate the performance of PMWN-based approach. The results show that the proposed approach outperforms PSM and Mb-ICP in terms of accuracy, efficiency, and loop closure error of mapping.

SYNCHRONIZING CHAOTIC ATTRACTORS OF CHUA'S CANONICAL CIRCUIT: THE CASE OF UNCERTAINTY IN CHAOS SYNCHRONIZATION

2006 ◽  
Vol 16 (07) ◽  
pp. 1961-1976 ◽  
Author(s):  
I. M. KYPRIANIDIS ◽  
A. N. BOGIATZI ◽  
M. PAPADOPOULOU ◽  
I. N. STOUBOULOS ◽  
G. N. BOGIATZIS ◽  
...  
Keyword(s):  
Coupling Strength ◽  
Chaos Synchronization ◽  
Phase Synchronization ◽  
Initial Conditions ◽  
Chaotic Synchronization ◽  
Chaotic Attractors ◽  
Coexisting Attractors

In this paper, we have studied the dynamics of two identical resistively coupled Chua's canonical circuits and have found that it is strongly affected by initial conditions, coupling strength and the presence of coexisting attractors. Depending on the coupling variable, chaotic synchronization has been observed both numerically and experimentally. Anti-phase synchronization has also been studied numerically clarifying some aspects of uncertainty in chaos synchronization.

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