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Bursting of Morris-Lecar neuronal model with current-feedback control

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中国科学:技术科学 2010年第3期 346-346页

The Morris-Lecar (ML) neuronal model with current-feedback control is considered as a typical fast-slow dynamical system to study the combined influences of the reversal potential VCa of Ca2+ and the feedback current I on the generation and transition of different bursting ***-parameter bifurcation analysis of the fast subsystem is performed in the parameter (I,VCa)-plane at *** important codimension-2 bifurcation points and some codimension-1 bifurcation curves are obtained which enable one to determine the parameter regions for different types of ***,we further divide the control parameter (V0,VCa)-plane into five different bursting regions,namely,the "fold/fold" bursting region R1,the "fold/Hopf" bursting region R2,the "fold/homoclinic" bursting region R3,the "subHopf/homoclinic" bursting region R4 and the "subHopf/subHopf" bursting region R5,as well as a silence region ***-1 and-2 bifurcations are responsible for explanation of transition mechanisms between different types of *** results are instructive for further understanding the dynamical behavior and mechanisms of complex firing activities and information processing in biological nervous systems.

关键词： neuron bursting bifurcation fast-slow dynamics analysis codimension

NONPARAMETRIC APPROACH TO IDENTIFYING NARX systems

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Journal of systems science & Complexity 2010年第1期23卷 3-21页

作者： Qijiang SONG·Han-Pu CHEN Key Laboratory of systems and Control,institute of systems science,academy of Mathematics and systems science,chinese academy of sciences,beijing 100190,china Key Laboratory of systems and Control Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

This paper considers identification of the nonlinear autoregression with exogenous inputs(NARX system).The growth rate of the nonlinear function is required be not faster than linear withslope less than *** value of f(·) at any fixed point is recursively estimated by the stochasticapproximation (SA) algorithm with the help of kernel *** consistency of the estimatesis established under reasonable conditions,which,in particular,imply stability of the *** simulation is consistent with the theoretical analysis.

关键词： α-mixing geometrically ergodic Markov chains NARX nonparametric recursive estimate stochastic approximation strongly consistent.

Remarks on Hard Lefschetz conjectures on Chow groups Dedicated in celebration of science china on the occasion of its 60th birthday

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science china Mathematics 2010年第1期53卷 105-114页

作者： FU BaoHua institute of Mathematics, academy of Mathematic and systems science, chinese academy of sciences, beijing 100190, china institute of Mathematics Academy of Mathematic and Systems Science Chinese Academy of Sciences Beijing China

We propose two conjectures of Hard Lefschetz type on Chow groups and prove them for some special cases. For abelian varieties, we show that they are equivalent to the well-known conjectures of Beauville and Murre.

关键词： Chow groups abelian varieties Bloch-Beilinson conjectures Beauville conjecture Murre conjecture

PROBABILISTIC NUMERICAL APPROACH FOR PDE AND ITS APPLICATION IN THE VALUATION OF EUROPEAN OPTIONS

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Journal of Computational Mathematics 2001年第6期19卷 591-600页

作者： Dong-sheng Wu (institute of systems science, academy of Mathematics and systems sciences, chinese academy of sciences, beijing 100080, china ) 中科院系统科学所北京 100080

Presents a probabilistic numerical approach for a class of probabilistic differential equation. Application of the Brownian motion and Monte-Carlo method; Application in the valuation of European Options.

关键词： Brownian motion probabilistic numerical solution European Options

Holomorphic invariant forms of a bounded domain

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science china Mathematics 2008年第11期51卷 1945-1964页

作者： LU QiKeng institute of Mathematics, academy of Mathematics and systems science, chinese academy of sciences, beijing 100190, china institute of Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

Given a complete ortho-normal system ? = (?0,?1,?2,…) of L 2 H( $ \mathcal{D} $ ), the space of holomorphic and absolutely square integrable functions in the bounded domain $ \mathcal{D} $ of ? n , we construct a holomorphic imbedding $ \iota _\phi :\mathcal{D} \to \mathfrak{F}(n,\infty ) $ , the complex infinite dimensional Grassmann manifold of rank n. It is known that in $ \mathfrak{F}(n,\infty ) $ there are n closed (μ, μ)-forms τμ (μ = 1,…,n) which are invariant under the holomorphic isometric automorphism of $ \mathfrak{F}(n,\infty ) $ and generate algebraically all the harmonic differential forms of $ \mathfrak{F}(n,\infty ) $ . So we obtain in $ \mathcal{D} $ a set of (μ, μ)-forms ι ? * τμ (μ = 1,…, n), which are independent of the system ? chosen and are invariant under the bi-holomorphic transformations of $ \mathcal{D} $ . Especially the differential metric ds 2 1 associated to the K?hler form ι ? * τ1 is a K?hler metric which differs from the Bergman metric ds 2 of $ \mathcal{D} $ in general, but in case that the Bergman metric is an Einstein metric, ds 1 2 differs from ds 2 only by a positive constant factor.

关键词： complete ortho-normal system holomorphic invariant forms 32A36 32A65

Study on the generator f of the operators I_n and I_t

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science china Mathematics 2010年第10期53卷 2589-2603页

作者： CHEN HanLin academy of Mathematics and systems science,chinese academy of sciences,beijing 100190,china academy of Mathematics and systems science Chinese Academy of Sciences Beijing China

Define two operators In and It,the inner product operator In(g)(x) := j∈Zs(g,f(·-j))f(x-j) and the interpolation operator It(g)(x) := j∈Zs g(j)f(x-j),where f belongs to some space and integer s *** call f the generator of the operators In and *** is well known that there are many results on operators In and *** there remain some important problems to be further *** application we first need to find the available generators (that can recover polynomials as It(p) = p or In(p) = p,p ∈Πm-1) for constructing the relative *** this paper,we focus on the available generator in the class of spline *** shall see that not all spline functions can be used to construct available ***,we do find a spline function in S,of degree m-1,where m is even and S is a class of *** for odd m the problem is still *** on spline functions in this paper are new.

关键词： generator available generator inner product operator spline interpolation operator two-closed refinable

CONVERGENCE AND SUPERCONVERGENCE OF HERMITE BICUBIC ELEMENT FOR EIGENVALUE PROBLEM OF THE BIHARMONIC EQUATION

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Journal of Computational Mathematics 2001年第2期19卷 139-142页

作者： Dong-sheng Wu (institute of systems science, academy of Mathematics and systems sciences, chinese academy of sciences, beijing 100080, china ) 中科院系统科学所北京 100080

Provides information on a study which discussed the convergence and superconvergence for eigenvalue problem of the biharmonic equation using the Hermite bicubic element. Discussion on eigenvalue problem for biharmonic equation; Background on asymptotic error expansions and interpolation postprocessing; Superconvergence approximations to the eigenvalue and eigenfunction.

关键词： Hermite bicubic element biharmonic equation interpolation postprocessing eigenvalue problem

The reason of Hopf’s and Oleinik’s proofs for countability of shocks being wrong

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science china Mathematics 2012年第4期55卷 727-729页

作者： LI BangHe academy of Mathematics and systems science,chinese academy of sciences,beijing 100190,china academy of Mathematics and systems science Chinese Academy of Sciences Beijing China

For the number of complete shock curves of a conservation law with one space variable,Hopf in 1950 for the Burger equation,and Oleinik in 1956 for the general,stated that it is at most *** 1979,the present author published an example to show that the statement of Hopf and Oleinik is *** after so long time,the wrong statement for countability still appeared in some publications,which is at least partly due to that some ones felt difficult to understand Hopf and Oleinik’s proofs being ***,pointing out where they went wrong becomes very necessary.

关键词： countability of shocks uncountability of shocks conservation law

MULTI-AGENT TRACKING OF A HIGH-DIMENSIONAL ACTIVE LEADER WITH SWITCHING TOPOLOGY

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Journal of systems science & Complexity 2009年第4期22卷 722-731页

作者： Yiguang HONG Xiaoli WANG Key Lab of systems and Control,institute of systems science,academy of Mathematics and systems science,chinese academy of sciences,beijing 100190,china. Key Lab of systems and Control Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

This paper considers a multi-agent tracking problem for a high-dimensional active leaderand variable interconnection topology. The state of the leader not only keeps changing but also maynot be measured. To estimate the state such a leader individually, a neighbor-based local controllertogether with a neighbor-based state-estimation rule is given for each autonomous agent. Then, theauthors prove that, with the help of a constructed common Lyapunov function (CLF), each agent cantrack the active leader with unmeasurable states. Finally, the authors explicitly construct a CLF foran active leader with unknown periodic input for illustration.

关键词： Active leader distributed algorithms multi-agent systems switching topology.