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topological horseshoe analysis and field-programmable gate array implementation of a fractional-order four-wing chaotic attractor

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Chinese Physics B 2018年第1期27卷 300-306页

作者：董恩增王震于晓陈增强王增会 Tianjin Key Laboratory For Control Theory & Applications in Complicated Systems Tianjin University of Technology Department of Automation Nankai University Department of Electrical and Mining Engineering University of South Africa

We present a fractional-order three-dimensional chaotic system, which can generate four-wing chaotic attractor. Dy- namics of the fractional-order system is investigated by numerical simulations. To rigorously verify the chaos properties of this system, the existence of horseshoe in the four-wing attractor is presented. Firstly, a Poincar6 section is selected properly, and a first-return Poincar6 map is established. Then, a one-dimensional tensile horseshoe is discovered, which verifies the chaos existence of the system in mathematical view. Finally, the fractional-order chaotic attractor is imple- mented physically with a field-programmable gate array （FPGA） chip, which is useful in further engineering applications of information encryption and secure communications.

关键词： fractional-order chaotic system Poincar6 map topological horseshoe field-programmable gatearray (FPGA)

Amplitude-Phase Modulation, topological horseshoe and Scaling Attractor of a Dynamical System

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Communications in Theoretical Physics 2016年第9期65卷 297-305页

作者：李春来李文张敬谢元喜赵益波 College of Physics and Electronics Hunan Institute of Science and Technology Yueyang 414006 China School of Electronic and Information Engineering Nanjing University of Information Science and Technology Nanjing 210044 China Jiangsu Collaborative Innovation Center on Atmospheric Environment and Equipment Nanjing Nanjing 210044 China

A three-dimensional autonomous chaotic system is discussed in this paper. Some basic dynamical properties of the system, including phase portrait, Poincar′e map, power spectrum, Kaplan–Yorke dimension, Lyapunov exponent spectra, signal amplitude and topological horseshoe are studied theoretically and numerically. The main finding by analysis is that the signal amplitude can be modulated via controlling the coefficients of the linear term, cross-product term and squared term simultaneously or respectively, and the phase of x3 can be modulated by the product of the coefficients of the linear term and cross-product term. Furthermore, scaling chaotic attractors of this system are achieved by modified projective synchronization with an optimization-based linear coupling method, which is safer for secure communications than the existed synchronization scheme since the scaling factors can be regarded as the security encoding key.

关键词： signal amplitude signal phase topological horseshoe scaling attractor

A New Proof for the Existence of topological horseshoe in a Business Cycle Model

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A New Proof for the Existence of Topological Horseshoe in a ...

horseshoe and entropy in a fractional-order unified system

2010 Chinese Control and Decision Conference

作者： Wenjuan Wu,Zengqiang Chen Department of Automation,Nankai University,Tianjin,300071

＜正＞Complex chaotic dynamics is studies in the van der Pol oscillator model of business cycle forced by a sinusoidal *** famous topological horseshoe theorem is applied to prove the existence of chaos from the mathematical viewpoint in this business cycle model.A rigorous proof for the existence of topological horseshoe is *** technique combines the topological theory with the computer-assisted computations.A proper Poincare section is first chosen to obtain the corresponding Poincare map,which is proved to be semi-conjugate to the 2-shift *** result implies that the business cycle model has positive topological entropy,and thus is definitely chaotic.

关键词： Chaos topological horseshoe Proof for the Existence Business Cycle Model

来源： cnki会议评论

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Chinese Physics B 2011年第1期20卷 175-180页

作者：李清都陈述周平 Key Laboratory of Networked Control and Intelligent Instrument of Ministry of Education Chongqing University of Posts and Telecommunications Institute for Nonlinear Systems Chongqing University of Posts and Telecommunications

This paper studies chaotic dynamics in a fractional-order unified system by means of topological horseshoe theory and numerical computation. First it finds four quadrilaterals in a carefully-chosen Poincare section, then shows that the corresponding map is semiconjugate to a shift map with four symbols. By estimating the topological entropy of the map and the original time-continuous system, it provides a computer assisted verification on existence of chaos in this system, which is much more convincible than the common method of Lyapunov exponents. This new method can potentially be used in rigorous studies of chaos in such a kind of system. This paper may be a start for proving a given fractional-order differential equation to be chaotic.

关键词： chaos topological horseshoe fractional-order system generalised Lorenz system

Chaos in a Simple Hopfield Neural Network Satisfying Dale’s Rule

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Chaos in a Simple Hopfield Neural Network Satisfying Dale’s...