OALib Journal期刊

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匹配条件: “徐健学” ,找到相关结果约110469条。
力学学报 , 2002, DOI: 10.6052/0459-1879-2002-1-2000-239
Abstract: 应用广义胞映射图论(GeneralizedCellMappingDigraph)方法,数值地研究Thompson的逃逸方程在最佳逃逸点附近的分岔.发现了嵌入在Wada分形吸引域边界上的混沌鞍,混沌鞍是状态空间不稳定(非吸引)的混沌不变集合,Wada分形吸引域边界是具有Wada性质的边界,即吸引域边界上的任意点也同时是至少两个其它吸引域的边界点,称为Wada域边界.我们证明Wada域边界上的混沌鞍导致局部鞍结分岔具有全局不确定性结局,研究了Wada域边界上混沌鞍的形成与演化,证明最终的逃逸分岔是混沌吸引子碰撞混沌鞍的边界激变.
力学学报 , 1999, DOI: 10.6052/0459-1879-1999-6-1995-086
Abstract: 应用广义胞映射理论的离散连续状态空间为胞状态空间的基本概念,依循Hsu的将偏序集和图论理论引入广义胞映射的思想,以集论和图论理论为基础,提出了进行非线性动力系统全局分析的广义胞映射图论方法.在胞状态空间上,定义二元关系,建立了广义胞映射动力系统与图的对应关系,给出了自循环胞集和永久自循环胞集存在判别定理的证明,这样可借助国论的理论和算法来确定动力系统的全局性质.应用图的压缩方法,对所有的自循环胞集压缩后,在全局瞬态分析计算中瞬态胞的总数目得到有效地减少,并能借助于图的算法有效地实现全局瞬态的拓扑排序.在整个定性性质的分析计算中,仅采用布尔运算.
力学学报 , 1994, DOI: 10.6052/0459-1879-1994-3-1995-551
Abstract: 本文用分叉理论的规范形方程设计和综合期望贮存静、动态记忆模式的神经网络。对于期望贮存静态记忆模式的网络,该规范形方程为叉形分叉的;若期望贮存的记忆模式是周期振荡形式,该规范形方程为高余维数Hopf分叉的,由满足设计约束的规范形系数得到的突触连接系数可以保证期望贮存的记忆模式都能成功地存贮于所设计的网络,且是网络仅有的吸引子,没有伪吸引子,吸引域的范围足够大。
宁夏医科大学学报 , 2007,
A chaotic saddle in a wada fractal basin boundary

Hong Ling Xu Jianxue,

力学学报 , 2002,
Abstract: In this paper, bifurcations near optimal escape for Thompson's escape equation are numerically studied by means of Generalized Cell Mapping Digraph (GCMD) method. We find a chaotic saddle embedded in a Wada fractal basin boundary. The chaotic saddle is an unstable (nonattracting) chaotic invariant set. The Wada fractal basin boundary has the Wada property that any point that is on the boundary of that basin is also simultaneously on the boundary of at least two other basins. The chaotic saddle in the Wada basin boundary plays an extremely important role in the bifurcations governing the escape. We demonstrate that the chaotic saddle in the Wada basin boundary leads to a local saddle-node fold bifurcation with globally indeterminate outcome. In such a case, the attractor (node) and the saddle of the saddle-node fold are merged into the chaotic saddle and the chaotic saddle also undergoes an abrupt enlargement in its size as a parameter passes through the bifurcation value, simultaneously the Wada basin boundary is also converted into the fractal basin boundary of two remaining attractors, in particular, the chaotic saddle after the saddle-node fold bifurcation is in the fractal basin boundary, this implies that the saddle-node fold bifurcation has indeterminate outcome, namely, after the system drifts through the bifurcation, which of the two remaining attractors the orbit goes to is indeterminate in that it is sensitively dependent on arbitrarily small effects such as how the parameter is changed and/or noise and/or computer roundoff, obviously, this presents an extreme form of indeterminacy in a dynamical system. We also investigate the origin and evolution of the chaotic saddle in the Wada basin boundary and demonstrate that the chaotic saddle in the Wada basin boundary is created by the collision between two chaotic saddles in different fractal basin boundaries. We demonstrate that a final escape bifurcation is the boundary crisis caused by the collision between a chaotic attractor and a chaotic saddle, and this implies that Grebogi's definition of the boundary crisis by the collision with a periodic saddle is generalized.

Xu Jianxue,Hong Ling,

力学学报 , 1999,
Abstract: In this paper, according to Hsu's idea that posets and digraphs are introduced intogeneralized cell mapping, a generalized cell mapping digraph method is presented by using thetheory of generalized cell mapping discretizing the continuous state space into the cell state spaceand the theories of set and digraph to achieve the task of global analysis of nonlinear dynamicalsystems. In the cell state space, we make the correspondence between generalized cell mappingdynamical systems and digraphs. The demonstrations of the two theorems of existence of self-cycling set and persistent self-cycling set are given. State cells are classified, and self-cycling sets,persistent self-cycling sets and transient self-cycling sets are defined. The persistent self-cycling setsrepresent the attractors of the systems, while the transient self-cycling sets are usually associatedwith the unstable fixed points and periodic solutions. Digraphs are introduced into generalizedcell mapping systems by defining binary relations in the cell state space, thus, the rich theoriesand the very powerful algorithms in the field of graphs and digraphs are adopted for the purposeof determing the global evolution properties of the systems. After all the self-cycling sets arecondensed by using digraph condensation method, the number of the state cells involved can beefficiently decreased in the global transient analysis, and a topological sorting of the global transientstate cells can be efficiently achieved by digraph algorithms, simultaneously, after transient cellsare classified to transient cell sets according to the number of the domiciles that they have, domainsof attraction and boundary regions can also be determined. Based on the different treatments,the global properties can be divided into qualitative (topological) and quantitative properties. Inthe whole analysis of the qualitative properties, only Boolean operations are used. The Booleanoperations are absolutely accurate, reliable, and time-saving. It is believed that the generalized cellmapping digraph method offers us a new way to examine the complicated behavior of nonlineardynamical systems.

力学学报 , 1998,
Abstract: Biological experiments of mammalian brain have shown that real neural systems exhibit a range of phenomena such as oscillations, phase-locking and even chaos. The chaotic behaviors simulate the information processing mechanisms of the real neural systems at a higher level. In this paper the bifurcation and chaos of the high order correlation networks will be studied.In some previous discussions about the high order correlation neural networks, we learned that the high order correlation networks expected to ...
The isolated critical value phenomenon in local-global riddling bifurcation
中国物理 B , 2002,
Abstract: A chaotic synchronized system of two coupled skew tent maps is discussed in this paper. The locally and globally riddled basins of the chaotic synchronized attractor are studied. It is found that there is a novel phenomenon in the local-global riddling bifurcation of the attractive basin of the chaotic synchronized attractor in some specific coupling intervals. The coupling parameter corresponding to the locally riddled basin has a single value which is embedded in the coupling parameter interval corresponding to the globally riddled basin, just like a breakpoint. Also, there is no relation between this phenomenon and the form of the chaotic synchronized attractor. This phenomenon is found analytically. We also try to explain it in a physical sense. It may be that the chaotic synchronized attractor is in the critical state, as it is infinitely close to the boundary of its attractive basin. We conjecture that this isolated critical value phenomenon will be common in a system with a chaotic attractor in the critical state, in spite of the system being discrete or differential.
An alternating periodic-chaotic ISI sequence of HH neuron under external sinusoidal stimulus
中国物理 B , 2004,
Abstract: A study of Hodgkin-Huxley (HH) neuron under external sinusoidal excited stimulus is presented in this paper. As is well known, the stimulus frequency is to be considered as a bifurcate parameter, and numerous phenomena, such as synchronization, period, and chaos appear alternatively with the changing of the stimulus frequency. For the stimulus frequency less than 2f_B (f_B being the base frequency in this paper), the simulation results demonstrate that the single HH neuron could completely convey the sinusoidal signal in anti-phase into interspike interval (ISI) sequences. We also report, perhaps for the first time, another kind of phenomenon, the beat phenomenon, which exists in the phase dynamics of the ISI sequences of the HH neuron stimulated by a sinusoidal current. It is shown furthermore that intermittent transition results in the general route to chaos.
冰川冻土 , 1997,
Abstract: 1997年4月15~17日在瑞典吕勒奥工学院召开了“国际地层冻结和冻结作用研讨会”.会议共发表论文82篇,涉及7个专题ISSMFE工作组报告、正冻正融土岩中的热质迁移、冻结敏感性和冻胀、已冻已融和正融土岩的力学性质、环境土冻结、工程设计和工程实例。文章主要论述土体冻结和冻胀研究的新进展。

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