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Complex transient dynamics of hidden attractors in a simple 4D system

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Chinese Physics B 2015年第5期24卷 270-274页

作者：党小宇李春彪包伯成武花干 College of Electronic and Information Engineering Nanjing University of Aeronautics and Astronautics School of Electronic & Information Engineering Nanjing University of Information Science & Technology School of Information Science and Engineering Changzhou University School of Electronic and Optical Engineering Nanjing University of Science and Technology

A simple four-dimensional system with only one control parameter is proposed in this paper. The novel system has a line or no equilibrium for the global control parameter and exhibits complex transient transition behaviors of hyperchaotic attractors, periodic orbits, and unstable sinks. Especially, for the nonzero-valued control parameter, there exists no equilibrium in the proposed system, leading to the formation of various hidden attractors with complex transient dynamics. The research results indicate that the dynamics of the system shows weak chaotic robustness and depends greatly on the initial states.

关键词： transient dynamics hidden attractor equilibrium

A novel memristive neural network with hidden attractors and its circuitry implementation

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Science China(Technological Sciences) 2016年第3期59卷 358-363页

作者： PHAM Viet Thanh JAFARI Sajad VAIDYANATHAN sundarapandian VOLOS Christos WANG Xiong School of Electronics and Telecommunications Hanoi University of Science and Technology Ol Dai Co Viet Hanoi Vietnam Biomedical Engineering Department Amirkabir University of Technology Tehran 15875-4413 Iran Research and Development Centre Vel Tech University Avadi Chennai-600062 Tamil Nadu India Physics Department Aristotle University of Thessaloniki GR-54124 Greece Institute for Advanced Study Shenzhen University Shenzhen 518060 China

Neural networks have been applied in various fields from signal processing, pattern recognition, associative memory to artifi- cial intelligence. Recently, nanoscale memristor has renewed interest in experimental realization of neural network. A neural network with a memristive synaptic weight is studied in this work. Dynamical properties of the proposed neural network are investigated through phase portraits, Poincar6 map, and Lyapunov exponents. Interestingly, the memristive neural network can generate hyperchaotic attractors without the presence of equilibrium points. Moreover, circuital implementation of such memristive neural network is presented to show its feasibility.

关键词： neural network memristor hyperchaos hidden attractor equilibrium

Design and multistability analysis of five-value memristor-based chaotic system with hidden attractors

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Chinese Physics B 2021年第10期30卷 207-218页

作者： Li-Lian Huang Shuai Liu Jian-Hong Xiang Lin-Yu Wang College of Information and Communication Engineering Harbin Engineering UniversityHarbin 150001China MIIT Key Laboratory of Advanced Marine Communication and Information Technology Harbin 150001China

A five-value memristor model is proposed,it is proved that the model has a typical hysteresis loop by analyzing the relationship between voltage and ***,based on the classical Liu-Chen system,a new memristor-based fourdimensional(4D)chaotic system is designed by using the five-value *** trajectory phase diagram,Poincare mapping,bifurcation diagram,and Lyapunov exponent spectrum are drawn by numerical *** is found that,in addition to the general chaos characteristics,the system has some special phenomena,such as hidden homogenous multistabilities,hidden heterogeneous multistabilities,and hidden ***,according to the dimensionless equation of the system,the circuit model of the system is built and *** results are consistent with the numerical simulation results,which proves the physical realizability of the five-value memristor-based chaotic system proposed in this paper.

关键词： five-valued memristor chaotic system hidden attractor multistability

Analysis and implementation of new fractional-order multi-scroll hidden attractors

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Chinese Physics B 2021年第2期30卷 203-210页

作者： Li Cui Wen-Hui Luo Qing-Li Ou Hunan University of Science and Technology Xiangtan 411201China

To improve the complexity of chaotic signals,in this paper we first put forward a new three-dimensional quadratic fractional-order multi-scroll hidden chaotic system,then we use the Adomian decomposition algorithm to solve the proposed fractional-order chaotic system and obtain the chaotic phase diagrams of different orders,as well as the Lyaponov exponent spectrum,bifurcation diagram,and SE complexity of the 0.99-order *** the process of analyzing the system,we find that the system possesses the dynamic behaviors of hidden attractors and hidden ***,we also propose a method of using the Lyapunov exponents to describe the basins of attraction of the chaotic system in the matlab environment for the first time,and obtain the basins of attraction under different order ***,we construct an analog circuit system of the fractional-order chaotic system by using an equivalent circuit module of the fractional-order integral operators,thus realizing the 0.9-order multi-scroll hidden chaotic attractors.

关键词： fractional order hidden attractor hidden bifurcation basins of attraction circuit implementation

Memristor hyperchaos in a generalized Kolmogorov-type system with extreme multistability

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Chinese Physics B 2023年第1期32卷 264-271页

作者：焦晓东袁明峰陶金孙昊孙青林陈增强 College of Artificial Intelligence Nankai UniversityTianjin 300350China Department of Earth and Space Science and Engineering York UniversityToronto M3 J 1P3Canada

Memristor chaotic systems have aroused great attention in recent years with their potentials expected in engineering *** this paper,a five-dimension(5D)double-memristor hyperchaotic system(DMHS)is modeled by introducing two active magnetron memristor models into the Kolmogorov-type *** boundness condition of the proposed hyperchaotic system is *** bifurcation diagram and numerical verification explain the *** rich dynamics of the system are demonstrated by the dynamic evolution map and the *** simulation results reveal the existence of transient hyperchaos and hidden extreme multistability in the presented *** NIST tests show that the generated signal sequence is highly random,which is feasible for encryption ***,the system is implemented based on a FPGA experimental platform,which benefits the further applications of the proposed hyperchaos.

关键词： extreme multistability memristor-based hyperchaos hidden attractor FPGA implementation

Generating hidden hyperchaos in a 5D hyperchaotic Burke-Shaw system with three positive Lyapunov exponents

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Generating hidden hyperchaos in a 5D hyperchaotic Burke-Shaw...

Analysis and Control of a Three-Dimensional Quadratic Polynomial System with No Equilibrium Point and No Linear Term

第十届动力学与控制学术会议

作者：魏周超张伟 J.C.Sprott Tomasz Kapitaniak School of Mathematics and Physics China University of Geosciences Division of Dynamics Technical University of Lodz College of Mechanical Engineering Beijing University of Technology Mathematical Institute University of Oxford Department of Physics University of Wisconsin

This paper reports the finding of hidden hyperchaos in a 5D hyperchaotic Burke-Shaw system, which is obtained by adding feedback controllers to the classic Burke-Shaw system. Of particular interest is that the hidden hyperchaotic attractors can be generated with three positive Lyapunov exponents in the proposed system with no equilibria or only two stable equilibria. The region of parameter space with bounded hidden solutions is relatively small, which accounts for the difficulty of surveying hidden attractors. Numerical analysis of phase trajectories, Lyapunov exponents, and Poincar′e map verify the existence of the hidden hyperchaotic attractors. As we know, the feature has not been previously reported in any other high dimensional *** it will represent a new type of hidden attractor with important and potentially problematic engineering consequences.

关键词： hidden attractor Hyperchaos No-equilibrium Stable equilibria Lyapunov exponents

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Analysis and Control of a Three-Dimensional Quadratic Polyno...

Stabilization of a Four-Dimensional Chaotic System with No Equilibria via a Novel Precise Constant-Control Approach

第32届中国控制与决策会议

作者： Zhongtang Chen Li Zheng Changchun Sun Shenyang Jianzhu University

A three-dimensional quadratic polynomial system with no equilibrium point and no linear term is derived in this paper.A new chaotic attractor can be generated from the ***,the existence of chaos is verified by calculating three Lyapunov *** behaviors of the system are analyzed in *** system does not have any equilibrium *** attractor generated from the system belongs to one of hidden *** diagrams of states are depicted respectively with the variation of two parameters.A problem on control of the polynomial system is investigated by employing constant control and state *** polynomial system with double symmetrical parameters is reported further.

关键词： Polynomial System Equilibrium Point Linear Term hidden attractor State Feedback

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Stabilization of a Four-Dimensional Chaotic System with No E...