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strange attractors ON PSEUDOSPECTRAL SOLUTIONS FOR DISSIPATIVE ZAKHAROV EQUATIONS1

Acta Mathematica Scientia 2004年第3期24卷 321-336页

作者： MaShuqing ChangQianshun InstituteofAppliedMathematics theChineseAcademyofSciencesBeijing100080China

In this paper, the pseudospectral method to solve the dissipative Zakharov equations is used. Its convergence is proved by priori estimates. The existence of the global attractors and the estimates of dimension are presented. A class of steady state solutions is also disscussed. The numerical results show that if the steady state solutions satisfy some special conditions, they become unstable and limit cycles and strange attractors will occur for very small *** largest Lyapunov exponent and analysis of the linearized system are applied to explain these phenomena.

关键词： strange attractors psendospectral method Zakharov equations

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SINAI BOWEN RUELLE MEASURE AND THE STRUCTURE OF strange attractors IN THE LAUWERIER MAP

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Applied Mathematics(A Journal of Chinese Universities) 2001年第1期16卷 25-34页

作者： Wang Yi\ Cao Yongluo Dept. of Math., Suzhou Univ., Suzhou 215006. Dept. of Math. Suzhou Univ. Suzhou

In this paper,the Lauwerier map F a,b (x,y)=(bx(1-2y)+y,ay(1-y)) is considered for a=4 . This map possesses a nontrivial topologically transitive attractor Λ which is the closure of the unstable set of some hyperbolic fixed point. Periodic points are dense in Λ and all of them are hyperbolic with eigenvalues uniformly bounded away from 1 in norm. Moreover,any two periodic points are heteroclinically related (transversal intersection of their stable and unstable sets). The Sinai Bowen Ruelle measure supported on the attractor is constructed and its properties are studied.

关键词： strange attractors Sinai Bowen Ruelle measure,transversal homoclinic point.

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Scaling Behaviour of Diffusion Limited Aggregation with Linear Seed

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Chinese Physics Letters 2006年第11期23卷 3033-3036页

作者：唐强田巨平姚凯伦 Department of Mathematics Wuhan University of Science and Engineering Wuhan 430073 Department of Physics Wuhan University of Science and Engineering Wuhan 430073 Research Center of Nonlinear Science Wuhan University of Science and Engineering Wuhan 430073 Department of Physics Huazhong University of Science and Technology Wuhan 430074 CCAST (World Laboratory) PO Box 8730 Beijing 100080

We present a computer model of diffusion limited aggregation with linear seed. The clusters with varying linear seed lengths are simulated, and their pattern structure, fractal dimension and multifractal spectrum are obtained. The simulation results show that the linear seed length has little effect on the pattern structure of the aggregation clusters if its length is comparatively shorter. With its increasing, the linear seed length has stronger effects on the pattern structure, while the dimension D f decreases. When the linear seed length is larger, the corresponding pattern structure is cross alike. The larger the linear seed length is, the more obvious the cross-like structure with more particles clustering at the two ends of the linear seed and along the vertical direction to the centre of the linear seed. Furthermore, the multifractal spectra curve becomes lower and the range of singularity narrower. The longer the length of a linear seed is, the less irregular and nonuniform the pattern becomes.

关键词： strange attractors

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THE FUZZY MODELING OF A CHAOTIC SYSTEM OF PERMANENT MAGNET SYNCHRONOUS MOTOR

THE FUZZY MODELING OF A CHAOTIC SYSTEM OF PERMANENT MAGNET S...

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第二十届中国控制会议

作者： Zhang Bo Li Zhong Mao Zong-yuan Power Electric College., South China University of Technology, Guangzhou, China, 510640 Dept. of Automatic Control Engineering, South China University of Technology, Guangzhou, China ,510640

＜正＞In this paper, a mathematical model of a permanent-magnet synchronous motor （PMSM） is derived, and the steady-state characteristics of this system, when subject to constant input voltages and constant external torque, are formulated. It is shown that the PMSM model can exhibit a variety of chaotic phenomena, under some choices of system parameters and external inputs. Based on TS fuzzy modeling methodology, the TS fuzzy model of the PMSM chaotic system is presented, so the interaction between fuzzy system and chaos can be explored, and then fuzzy-model-based control methodologies can be used to control chaos in chaotic systems. Computer simulations show that the strange attractors in the derived TS fuzzy system and original chaotic system are topologically equivalent.

关键词： Fuzzy modeling, permanent-magnet synchronous motors, TS fuzzy model chaos strange attractors

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