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What Does Dynamical Systems Theory Teach Us about Fluids?

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Communications in Theoretical Physics 2014年第10期61卷 451-468页

作者： Hadrien Bosetti Harald A.Posch Computational Physics Group Faculty of PhysicsUniversity of Vienna Boltzmanngasse 51090 WienAustria Complex Energy Systems Group Austrian Institute of Technology Giefinggasse 61210 WienAustria

We use molecular dynamics simulations to compute the lyapunov spectra of many-particle systems resembling simple fluids in thermal equilibrium and in non-equilibrium stationary states. Here we review some of the most ... 详细信息

关键词： dynamical system theory lyapunov instability hydrodynamic modes phase transitions stationary nonequilibrium states

Practical stabilization of receding-horizon control

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Journal of Central South University of Technology 2001年第4期8卷 268-271页

作者： LIU Bi yu,GUI Wei hua,MU Min (College of Information Science and Engineering, Central South University, Changsha 410083, China) College of Information Science and Engineering Central South University Changsha China

The purpose of this work is to propose a scheme to stabilize the predictive control systems in the practical stability sense. In the paper, the authors dealt with a general discrete predictive control system x j+1|t =f(x j|t , u j|t ) by using the lyapunov direct method combining with receding horizon control technique, and presented a new condition to guarantee the practical stabilization of the systems. With the proposed results, one can design the optimal controllers easily to practically stabilize the predictive control systems.

关键词： receding-horizon control practical stability lyapunov function nonlinear system optimization

ON KOLMOGOROV ENTROPY OF SOME MEASURE-PRESERVING MAPPINGS

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Science China Mathematics 1991年第2期34卷 214-219页

作者：严志明孙义燧 Department of Astronomy Nanjing University Nanjing 210008 PRC

In this paper, we calculate Kolmogorov entropies (K-entropies) of a 2-dimensional mappingwith a hyperbolic fixed point and its perturbed extension to 3-dimensional:T: x_(n+1)=s(x_ncosψ_n-y_nsinψ_n)+Acosz_n, y_(n+1)=s^(-1)(x_nsinψ_n+y_ncosψ_n)+Bsinz_n, z_(n+1)=z_n+Ccos(x_(n+1)+y_(n+1)) + D, (mod 2π),ψ_n = (x_n^2+y_n^2)~*** variation of K-entropies with parameters have been obtained. The results show thatthe hyperbolicity of the fixed point and the negative k play a more important role in gene-rating the stochasticity of the motion than the other parameters.

关键词： hyperbolic twist mapping perturbed extension lyapunov characteristic number Kolmogorov entropy.

Nonlinear feedback control of Timoshenko beam

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Science China Mathematics 1995年第8期38卷 918-927页

作者：冯德兴张维弢 Institute of Systems Science. Chinese Academy of Sciences Beijing 100080 China

This note is concerned with nonlinear boundary feedback control of a Timoshenko beam. Under some nonlinear boundary feedback control, first the nonlinear semigroup theory is used to show the existence and uniqueness of solution for the corresponding closed loop system. Then by using the lyapunov method, it is proved that the vibration of the beam under the proposed control action decays in a negative power of time t as t→.

关键词： Timoshenko beam boundary feedback control nonlinear semigroup lyapunov method.

RUELLE'S INEQUALITY FOR THE ENTROPY OF RANDOM DIFFEOMORPHISMS

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Science China Mathematics 1992年第9期35卷 1056-1065页

作者：龚光鲁刘培东钱敏 Department of Applied Mathematics Tsinghua University Beijing 100084 PRC Department of Mathematics Peking University Beiiing 100871 PRC

In this paper, we prove Ruelle’s inequality for the entropy and lyapunov exponents of random diffeomorphisms. Y. Kefer has studied this problem in ergodic case, but his theorem and proof seem to be incorrect. A new discussion is given in this paper with some new ideas and methods to be introduced, especially for f∈Diff^2(M), we introduce a new definition of C^2-norm |f|c^2 and the concept of relation number r(f) which play an important role both in this paper and in general studies.

关键词： entropy lyapunov exponent C^2-norm |f|_c^2 relation number r(f).

A new complex Duffing oscillator used in complex signal detection

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Chinese Science Bulletin 2012年第17期57卷 2185-2191页

作者： DENG XlaoYing LIU HaiBo LONG Teng School of in formation and Electronics Beijing Institute of TechnologyBeijing 100081China

In view of the fact that complex signals are often used in the digital processing of certain systems such as digital communication and radar systems,a new complex Duffing equation is *** addition,the dynamical behaviors are *** calculating the maximal lyapunov exponent and power spectrum,we prove that the proposed complex differential equation has a chaotic solution or a large-scale periodic one depending on different *** on the proposed equation,we present a complex chaotic oscillator detection system of the Duffing *** a dynamic system is sensitive to the initial conditions and highly immune to complex white Gaussian noise,so it can be used to detect a weak complex signal against a background of strong *** of the Monte-Carlo simulation show that the proposed detection system can effectively detect complex single frequency signals and linear frequency modulation signals with a guaranteed low false alarm rate.

关键词：信号检测 Duffing方程振荡器 lyapunov 复域雷达系统线性调频信号检测系统

Hybrid Adaptive Compensation Control Scheme for High-Precision Servo System

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Transactions of Tianjin University 2013年第3期19卷 217-224页

作者：扈宏杰王元哲孙国伟 School of Automation Science and Electrical Engineering Beihang University Science and Technology on Aircraft Control Laboratory Beihang University

In this paper,a hybrid adaptive compensation control scheme is proposed to compensate the friction occurrence and other nonlinear disturbance factors that exist in the high-precision servo *** adaptive compensation controller with a dual-observer structure is designed,while the LuGre dynamic friction model with non-uniform parametric uncertainties characterizes the friction *** the influence of the periodic disturbance torque and parametric uncertainties,fuzzy systems and a robust term are *** this way,the whole system can be treated as a simple linear model after being compensated,then the proportional-derivative (PD) control law is applied to enhancing the control *** the basis of lyapunov stability theory,the global stability and the asymptotic convergence of the tracking error are *** simulations demonstrate that the proposed scheme has potentials to restrain the impact of disturbance and improving the tracking performance.

关键词： servo system LuGre model friction observer fuzzy system adaptive control lyapunov stability

Stationary distribution and periodic solution of stochastic chemostat models with single-species growth on two nutrients

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International Journal of Biomathematics 2019年第6期12卷 23-41页

作者： Miaomiao Gao Daqing Jiang Taxawar Haya College of Science China University o/Petroleum(Haul China)Qingdao 266580P.R.China Keg laboratory of Unconventional Oil and Cos Development China University of Petroleum(East China)Ministry of Education.Qingdao 260580.P.It.China Nonlinear Analysis and Applied Mathematics(NAAM)-Research Group Department of Mathematics.King Abdulaziz University Jeddah 21589 Saudi Arabia Department of Mathematics Quaid-I-Azam University 45320 Islamabad 44000.Pakistan

In this paper,we consider two chemostat models w th random perturbation,in which single species depends on two perfectly substitutable resources for *** the autonomous system,we first prove that the solution of the system is positive and *** we establish sufficient conditions for the existence of an ergodic stationary distribu tion by constructing appropriate lyapunov functions-For the non-autonomous system,by using Mas'minskii theory on periodic Markov processes,we derive it admits a nontriv ial positive periodic ***,numerical simulations are carried out to illustrate our main results.

关键词： Chemostat model lyapunov function stationary distribution Markov pro cess periodic solution.

Partial stability analysis of nonlinear time-varying impulsive systems

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International Journal of Biomathematics 2019年第6期12卷 73-98页

作者： Boulbaba Ghanmi Faculty of Sciences of Gafsa University of GafsaSidi Ahmed Zarroug 2112GafsaTunisia

This paper investigates the stability analysis with respect to part of the variables of nonlinear time-varying systems with impulse *** approach presented is based on the specially introduced piecewise continuous lyapunov *** lyapunov stability theorems with respect to part of the variables are generalized in the sense that the time derivatives of the lyapunov functions are allowed to be *** the help of the notion of stable functions,asymptotic partial stability,exponential partial stability,input-to-state partial stability(ISPS)and integral input-to-state partial stability(iISPS)are *** numerical examples are provided to illustrate the effectiveness of the proposed theoretical results.

关键词： Nonlinear impulsive systems partial stability piecewise continuous scalar functions indefinite lyapunov function input-to-state partial stability(ISPS) integral input-to-state partial stability(iISPS).