Periodic offset boosting for attractor self-reproducing

2021 ◽  
Vol 31 (11) ◽  
pp. 113108
Author(s):  
Chunbiao Li ◽  
Yicheng Jiang ◽  
Ran Wang ◽  
Zuohua Liu
Keyword(s):  
Offset Boosting

Hidden Extreme Multistability, Antimonotonicity and Offset Boosting Control in a Novel Fractional-Order Hyperchaotic System Without Equilibrium

2018 ◽  
Vol 28 (13) ◽  
pp. 1850167 ◽  
Author(s):  
Sen Zhang ◽  
Yicheng Zeng ◽  
Zhijun Li ◽  
Chengyi Zhou
Keyword(s):  
Fractional Order ◽  
Initial Conditions ◽  
State Feedback Control ◽  
Hyperchaotic System ◽  
Hidden Attractors ◽  
System Parameters ◽  
Offset Boosting ◽  
Extreme Multistability ◽  
Hidden Extreme Multistability ◽  
New System

Recently, the notion of hidden extreme multistability and hidden attractors is very attractive in chaos theory and nonlinear dynamics. In this paper, by utilizing a simple state feedback control technique, a novel 4D fractional-order hyperchaotic system is introduced. Of particular interest is that this new system has no equilibrium, which indicates that its attractors are all hidden and thus Shil’nikov method cannot be applied to prove the existence of chaos for lacking hetero-clinic or homo-clinic orbits. Compared with other fractional-order chaotic or hyperchaotic systems, this new system possesses three unique and remarkable features: (i) The amazing and interesting phenomenon of the coexistence of infinitely many hidden attractors with respect to same system parameters and different initial conditions is observed, meaning that hidden extreme multistability arises. (ii) By varying the initial conditions and selecting appropriate system parameters, the striking phenomenon of antimonotonicity is first discovered, especially in such a fractional-order hyperchaotic system without equilibrium. (iii) An attractive special feature of the convenience of offset boosting control of the system is also revealed. The complex and rich hidden dynamic behaviors of this system are investigated by using conventional nonlinear analysis tools, including equilibrium stability, phase portraits, bifurcation diagram, Lyapunov exponents, spectral entropy complexity, and so on. Furthermore, a hardware electronic circuit is designed and implemented. The hardware experimental results and the numerical simulations of the same system on the Matlab platform are well consistent with each other, which demonstrates the feasibility of this new fractional-order hyperchaotic system.

Periodically varied initial offset boosting behaviors in a memristive system with cosine memductance

2019 ◽  
Vol 20 (12) ◽  
pp. 1706-1716 ◽  
Author(s):  
Mo Chen ◽  
Xue Ren ◽  
Hua-Gan Wu ◽  
Quan Xu ◽  
Bo-cheng Bao
Keyword(s):  
Offset Boosting ◽  
Memristive System

Interpreting initial offset boosting via reconstitution in integral domain

2020 ◽  
Vol 131 ◽  
pp. 109544 ◽  
Author(s):  
Mo Chen ◽  
Xue Ren ◽  
Huagan Wu ◽  
Quan Xu ◽  
Bocheng Bao
Keyword(s):  
Integral Domain ◽  
Offset Boosting

Dynamics editing based on offset boosting

2020 ◽  
Vol 30 (6) ◽  
pp. 063124
Author(s):  
Chunbiao Li ◽  
Tengfei Lei ◽  
Xiong Wang ◽  
Guanrong Chen
Keyword(s):  
Offset Boosting

Diagnosing multistability by offset boosting

2017 ◽  
Vol 90 (2) ◽  
pp. 1335-1341 ◽  
Author(s):  
Chunbiao Li ◽  
Xiong Wang ◽  
Guanrong Chen
Keyword(s):  
Offset Boosting

scholarly journals Generating novel multi-scroll chaotic attractors via fractal transformation

2021 ◽  
Author(s):  
Dengwei Yan ◽  
Musha Ji’e ◽  
Lidan Wang ◽  
Shukai Duan ◽  
Xinyu Du
Keyword(s):  
Efficient Method ◽  
Theoretical Basis ◽  
Chaotic Systems ◽  
Chaotic Attractors ◽  
Hardware Platform ◽  
New Class ◽  
Chaotic Sequences ◽  
Offset Boosting ◽  
Before And After ◽  
First Time

Abstract The fractal and chaos are bound tightly, and their relevant researches are well-established. Few of them, however, concentrates on the research of the possibility of combining the fractal and the chaotic systems to generate multi-scroll chaotic attractors. This paper presents a novel non-equilibrium point chaotic system, exhibiting extremely rich and complex hidden behaviors including chaos, hyper-chaos, multi-scroll attractors, extreme multi-stability and initial offset-boosting. The proposed system is combined with fractal transformation respectively, and a new class of multi-scroll attractors, such as multi-ring attractors and separated-scroll attractors, is observed. Particularly, swallow-shaped attractors for the first time is found. Moreover, another efficient method to generate a different class of chaotic attractors uses parabola transformation and triangle transformation. Additionally, the spectrum entropy ( SE ) complexity is employed to discuss the complexity of the proposed system before and after fractal, resulting in a chaotic sequences with fractal transformation that has higher complexity. Finally, we develop a hardware platform to implement the presented attractors before and after fractal in a way to confirm the accuracy of the numerical simulations, providing a theoretical basis for the next application in image encryption.

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

scholarly journals Conditional Symmetry of a Memristive System with Amplitude and Frequency Modulation Control

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Hongyan Zang ◽  
Lili Huang ◽  
Tengfei Lei ◽  
Yanling Wang
Keyword(s):  
Frequency Control ◽  
Symmetric System ◽  
Conditional Symmetry ◽  
Asymmetric System ◽  
System A ◽  
Offset Boosting ◽  
Memristive System ◽  
Modulation Control ◽  
Amplitude And Frequency Modulation ◽  
Multiple Stability

In this study, we studied the effects of offset boosting on the memristive chaotic system. A system with symmetry and conditional symmetry was constructed, by adding the absolute value function to an offset boosting system. It is proved that the symmetric system or a conditionally symmetric system can be constructed with similar or the same dynamic characteristics by using certain correction and offset boosting in an asymmetric system. In addition to multiple stability, the memristive system can also realize the amplitude and frequency control by introducing a parameter. The simulation circuit verifies the amplitude modulation characteristics of the system.

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