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.

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.

Offset Boosting for Breeding Conditional Symmetry

2018 ◽  
Vol 28 (14) ◽  
pp. 1850163 ◽  
Author(s):  
Chunbiao Li ◽  
Julien Clinton Sprott ◽  
Yongjian Liu ◽  
Zhenyu Gu ◽  
Jingwei Zhang
Keyword(s):  
Chaotic Systems ◽  
Basin Of Attraction ◽  
Two Dimensions ◽  
Symmetric Pair ◽  
Conditional Symmetry ◽  
Coexisting Attractors ◽  
One Dimensional ◽  
Offset Boosting ◽  
The Basin Of Attraction ◽  
General Method

Symmetry is usually prevented by the broken balance in polarity. If the offset boosting returns the balance of polarity when some of the variables have their polarity reversed, the corresponding system becomes conditionally symmetric and in turn produces coexisting attractors with that type of symmetry. In this paper, offset boosting in one dimension or in two dimensions in a 3D system is made for producing conditional symmetry, where the symmetric pair of coexisting attractors exist from one-dimensional or two-dimensional offset boosting, which is identified by the basin of attraction. The polarity revision from offset boosting provides a general method for constructing chaotic systems with conditional symmetry. Circuit implementation based on FPGA verifies the coexisting attractors with conditional symmetry.

scholarly journals Symmetry Evolution in Chaotic System

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 574 ◽  
Author(s):  
Chunbiao Li ◽  
Jiayu Sun ◽  
Tianai Lu ◽  
Tengfei Lei
Keyword(s):  
Dynamical System ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
System Transformation ◽  
Conditional Symmetry ◽  
Offset Boosting ◽  
Key Factor

A comprehensive exploration of symmetry and conditional symmetry is made from the evolution of symmetry. Unlike other chaotic systems of conditional symmetry, in this work it is derived from the symmetric diffusionless Lorenz system. Transformation from symmetry and asymmetry to conditional symmetry is examined by constant planting and dimension growth, which proves that the offset boosting of some necessary variables is the key factor for reestablishing polarity balance in a dynamical system.

Time-Reversible Chaotic System with Conditional Symmetry

2020 ◽  
Vol 30 (05) ◽  
pp. 2050067 ◽  
Author(s):  
Chunbiao Li ◽  
Julien Clinton Sprott ◽  
Yongjian Liu
Keyword(s):  
Numerical Analysis ◽  
Chaotic System ◽  
Fundamental Property ◽  
Reversible Systems ◽  
Reversible System ◽  
Conditional Symmetry ◽  
Coexisting Attractors ◽  
Offset Boosting ◽  
Time Domains ◽  
System Attractor

When the polarity reversal induced by offset boosting is considered, a new regime of a time-reversible chaotic system with conditional symmetry is found, and some new time-reversible systems are revealed based on multiple dimensional offset boosting. Numerical analysis shows that the system attractor and repellor have their own dynamics in respective time domains which constitutes the fundamental property in a time-reversible system. More remarkably, when the conditional symmetry is destroyed by a slightly mismatched offset controller, the system undergoes different bifurcations to chaos, and the corresponding coexisting attractors and repellors shape their own phase trajectories.

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 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.

Various Attractors, Coexisting Attractors and Antimonotonicity in a Simple Fourth-Order Memristive Twin-T Oscillator

2018 ◽  
Vol 28 (04) ◽  
pp. 1850050 ◽  
Author(s):  
Ling Zhou ◽  
Chunhua Wang ◽  
Xin Zhang ◽  
Wei Yao
Keyword(s):  
Fourth Order ◽  
Chaotic Systems ◽  
Basin Of Attraction ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Coexisting Attractors ◽  
Dynamical Behaviors ◽  
Random Bit Generator ◽  
In Series ◽  
Dynamical Features

By replacing the resistor in a Twin-T network with a generalized flux-controlled memristor, this paper proposes a simple fourth-order memristive Twin-T oscillator. Rich dynamical behaviors can be observed in the dynamical system. The most striking feature is that this system has various periodic orbits and various chaotic attractors generated by adjusting parameter [Formula: see text]. At the same time, coexisting attractors and antimonotonicity are also detected (especially, two full Feigenbaum remerging trees in series are observed in such autonomous chaotic systems). Their dynamical features are analyzed by phase portraits, Lyapunov exponents, bifurcation diagrams and basin of attraction. Moreover, hardware experiments on a breadboard are carried out. Experimental measurements are in accordance with the simulation results. Finally, a multi-channel random bit generator is designed for encryption applications. Numerical results illustrate the usefulness of the random bit generator.

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.

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