徐健学
非线动力学现代理论，生物神经放电非线性动力学行为和神经信息编码，转子动力学，电磁固体、流体固体耦合振动和控制
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 姓名：徐健学
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学术头衔：
博士生导师，
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学科领域：
基础力学
 研究兴趣：非线动力学现代理论，生物神经放电非线性动力学行为和神经信息编码，转子动力学，电磁固体、流体固体耦合振动和控制
徐健学，1933年出生，1956年交通大学机械系毕业，留校任教，1986年任教授，1990年任博士生导师，2005年退休。现任西安交通大学校学术委员会委员、中国力学学会一般力学专业委员会委员、中国振动工程学会非线性振动专业委员会委员，《动力学与控制》和国际期刊《Cognitive Neurodynamics》编委.从事一般力学、多交叉学科的基础和应用基础的教学和研究，熟悉的领域有：非线动力学现代理论，生物神经放电非线性动力学行为和神经信息编码，转子动力学，电磁固体、流体固体耦合振动和控制。讲授和开设本科和研究生课程11门；指导硕士、博士研究生45名；主持完成国家自然科学基金项目6项，参加完成和在研重大重点国家自然科学基金、863、七五、八五攻关等科研10项。多次被邀请在国际会议做主旨报告，出国讲学。曾为美国伯克莱加利福尼亚大学访问学者、名古屋工业大学日本文部省聘任教授，曾任西安交通大学建筑工程与力学学院非线性动力学所所长、西安交通大学非线性科学中心(虚拟)主任。所指导的博士生龚云帆的学位论文被评为2001年全国百篇优秀博士学位论文；洪灵的博士学位论文被评为2004年全国百篇优秀博士学位论文提名。独立和合作，国际学术刊物发表论文49篇，中国学术刊物发表论文150篇，国际会议论文56篇，出版著作3部；论文被SCI收录80篇、SCI引用 201次，其他国际国内索引刊物333次。 “复杂非线性系统的动力学理论与方法” 获2003年国家自然科学奖二等奖，“离相封闭母线理论与实践” 获1987年国家科技进步三等奖，及获省部级自然科学奖和科技进步奖6项。
主要理论和应用进展为：
1.高维非线性动力系统分岔、全局分析，筛形吸引域，Wada吸引域，偏序集图论广义胞映射法改进，激变的与混沌鞍碰撞机制.
2.极限环双稳态随机共振新机制，二维系统随机共振的解析结果。
3.生物神经动力学方法，大鼠损伤神经放电峰峰间期序列的确定性混沌、动物癫痫皮层脑电预报等现象和机理
4.封闭母线、大型变压器电磁机械相关理论和试验，用于葛洲坝电站和武钢轧机重大工程，机组电网耦联次同步共振，高温堆蒸发器流弹不稳定性，混沌同步通讯伪装的破译。
国际学术界同行给出：位于前沿、非常重要的新发现优秀和创新工作等评价。

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7
徐健学， YanMei Kang， *， JianXue Xu， †， and Yong Xie‡
PHYSICAL REVIEW E 68, 036123 (2003)，0001，（）：
1年11月30日
The method of moments is applied to an underdamped bistable oscillator driven by Gaussian white noise and a weak periodic force for the observations of stochastic resonance and the resulting resonant structures are compared with those from Langevin simulation. The physical mechanisms of the stochastic resonance are explained based on the evolution of the intrawell frequency peak and the abovebarrier frequency peak via the noise intensity and the fluctuationdissipation theorem, and the three possible sources of stochastic resonance in the system are confirmed. Additionally, with the noise intensity fixed, the stochastic resonant structures are also observed by adjusting the nonlinear parameter.

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徐健学， JianXue Xu*， Hong Huang， PeiZhen Zhang， JiQing Zhou
nternational Journal of NonLinear Mechanics 37(2002)909920，0001，（）：
1年11月30日
In this paper, the dynamic stability of a shallowarch with elastic supports subjected to impulsive load is used as a theoretical model to investigate the dynamic stability problem of inner windings of power transformer under shortcircuit condition. Firstly, the series solution representing the equilibrium conogurations of a shallowarch is obtained by solving the corresponding nonlinear integrationdi1erential equation. The local stability of each equilibrium conoguration is discussed, and the sucient condition for stability of the shallowarch system as well as the critical load against snapthrough is obtained. Secondly, the equivalent relation between shortcircuit load and impulsive one, and the electrical forces transferred pattern between the coils of inner windings are assumed. Then the results of the shallowarch model are applied to the case of the inner winding of transformer and the formulas for computing critical electromagnetic force and the dynamic stability criterion of the inner windings are established. Finally, examples are o1ered and the theoretical results are shown to agree well with the experimental ones.
Shallowarch， Dynamic stability， Snapthrough， Transformer， Short circuit

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【期刊论文】Global dynamics and stochastic resonance of the forced FitzHughNagumo neuron model
徐健学， PuLin Gong and JianXue Xu
PHYSICAL REVIEW E, VOLUME 63, 031906，0001，（）：
1年11月30日
We have analyzed the responses of an excitable FitzHughNagumo neuron model to a weak periodic signal with and without noise. In contrast to previous studies which have dealt with stochastic resonance in the excitable model when the model with periodic input has only one stable attractor, we have focused our attention on the relationship between the global dynamics of the forced excitable neuron model and stochastic resonance. Our results show that for some parameters the forced FitzHughNagumo neuron model has two attractors: the smallamplitude subthreshold periodic oscillation and the largeamplitude suprathreshold periodic oscillation. Random transitions between these two periodic oscillations are the essential mechanism underlying stochastic resonance in this model. Differences of such stochastic resonance to that in a classical bistable system and the excitable system are discussed. We also report that the state of the basin of attraction has a significant effect on the stability of neuronal firings, in the sense that the fractal basin boundary of the system enhances the noiseinduced transitions.

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【期刊论文】Crises and chaotic transients studied by the generalized cell mapping digraph method
徐健学， Ling Hong*， Jianxue Xu
Physics Letters A 262 1999. 361375，0001，（）：
1年11月30日
In this Letter, a generalized cell mapping digraph method is presented on the basis of a correspondence between the generalized cell mapping of dynamical systems and digraphs, and this correspondence is theoretically proved on the basis of set theory in the cell state space. State cells are classified afresh, and selfcycling sets, persistent selfcycling sets and transient selfcycling sets are defined. The algorithms of digraphs are adopted for the purpose of determining the global evolution properties of the systems. After all the selfcycling sets are condensed by using the digraphic condensation method, a topological sorting of the global transient state cells can be efficiently achieved. Based on the different treatments, the global properties can be divided into qualitative and quantitative properties. In the analysis of the qualitative properties, only Boolean operations are used. As a result, the complicated behavior of nonlinear dynamical systems can be efficiently studied in a new way. A boundary crisis is studied by means of the generalized cell mapping digraph method. Attractors, basins, basin boundaries and unstable solutions are obtained once through a global analysis at low computational cost. Moreover, the approach of a chaotic attractor to an unstable periodic orbit at its basin boundary before a boundary crisis, the collision of the chaotic attractor with the unstable periodic orbit when the crisis occurs, and a chaotic transient after the crisis, are explicitly shown. The limiting probability distribution of the chaotic attractor is calculated.
Global analysis， Generalized cell mapping of dynamical system， Set， Digraph， Topological sorting， Chaotic transient， Crisis， Markov chain

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【期刊论文】THE PROBLEM OF AN ELASTICPLASTIC BEAM DYNAMICS AND AN INCOMPLETE CODIMENSION TWO BIFURCATION
徐健学， JianXue Xu* and Norio Hasebe
lnt J. NonLinear Mechanics, Vol. 32, No.1, pp. 127143, 1997，0001，（）：
1年11月30日
ln this paper, a continuous fourthorder ordinary differential equation Shanleytype model is suggested for analytical analysis of the problem of elasticplastic beam dynamics. A codimension three bifurcation problem and its simplified case, an incomplete codimension two bifurcation of a pair of pure imaginary eigenvalues and a simple zero eigenvalue are presented and analyzed, and the normal form analysis and the unfoldings of 2jet and 4jet cases of the incomplete normal forms are provided. Since elasticPlastic beam dynamics are of great nonlinear complexity and the vector fields are multiple degeneracies, small differences of physical parameters cause dramatic essential changes of behavior of the motion. Through these results the rich dynamical behaviors of the elastic plastic beam dynamics, including the counterintuitive behavior and its sensitivity to small parameters of this problem, can be illustrated. Copyright.
Shanleytype model,， high codimension bifurcation,， normal form,， unfolding,， degenerate singularity

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【期刊论文】Propagation of periodic and chaotic action potential trains along nerve fibers
徐健学， Xu Jianxuea， Gong Yunfana， *， Ren Weib， Hu Sanjueb， Wang Fuzhoub
Physica D 100(1997)212224，0001，（）：
1年11月30日
In this paper, we report the findings that the action potential trains transmitted along the nerve fibers are encoded not only periodically but also chaotically. First, spontaneous action potentials along a single fiber of injured sciatic nerves in the., anesthetized rat were recorded. Then, the data were divided into two groups and analyzed with different methods. Phase space: representation, spectral analysis and the calculation of correlation dimension were used for the first group of data sampled with constant frequency. Due to the serious influence of the measurement noise, no reliable conclusion can be drawn from them. For the second group of data of the interspike intervals (ISI) which seem to convey more rich and important information. nonlinear forecasting method, the surrogate data and the plot of ISI (n+1) vs. ISI (n) were used in the analysis, good results have been obtained which confirm with those from the/3cell model. The largest Lyapunov exponent (LLE) were calculated not only to further support our findings of chaos but also to quantitatively determine the degree of chaos.
Neural electrophysiological activities， ISI time series， Chaos， Nonlinear forecasting method， The surrogate data， Largest Lyapunov exponent

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【期刊论文】The Global Bifurcation Characteristics of the Forced van der Pol Oscillator
徐健学， JIANXUE XU and JUN JIANG
chaos, Solitons & Fractals Vol. 7, No.1, pp. 319, 1996，0001，（）：
1年11月30日
In this paper, the bifurcation characteristics of the forced van der Pol oscillator on a specific parameter plane, including intermediate parameter regions, are investigated. The successive arrangement of the dominant modelocking regions, where a single subharmonic solution with the rotation number, 1/(2k+1), exists, and the transitional zones between them are depicted. The transitional zones are explicitly proposed to be classified into two groups according to the different global characters:(1) the simple transitional zones, in which coexistence of two modelocked solutions with rotation numbers 1/(2k+1) appear; (2) the complex transitional zones, in which the subzones with the modelocked solutions, whose rotation numbers are rational fractions between 1/(2k+1) and 1/(2k1), and the quasiperiodic solutions exist. The emphasis of this paper is to study the evolution of the global structures in the transitional zones. A complex transitional zone generally evolves from a Farey tree, when the forcing amplitude is small, to a chaotic regime, when forcing amplitude is sufficiently large. It is of great interest that the subzone with a rotation number, 1/2k, which has the largest width within a complex transitional zone, can usually intrude into the dominant regions of 1/(2k1) before it completely vanishes. Moreover, the features of overlaps of modelocking subzones and the number of coexistence of different attractors are also discussed.

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