应用广义胞映射图论方法(GCMD)研究SD(smooth and discontinuous systems)振子的内部激变现象.通过对SD常微分方程系统的全局分析发现周期解通向混沌的内部激变现象是由于周期吸引子与在其吸引域内部的混沌鞍碰撞产生的.混沌鞍是胞空间...应用广义胞映射图论方法(GCMD)研究SD(smooth and discontinuous systems)振子的内部激变现象.通过对SD常微分方程系统的全局分析发现周期解通向混沌的内部激变现象是由于周期吸引子与在其吸引域内部的混沌鞍碰撞产生的.混沌鞍是胞空间中的瞬态自循环胞集,周期吸引子与混沌鞍发生碰撞后,混沌鞍转化为混沌吸引子新增的一部分;内部激变不会改变原来吸引域的形状且具有可逆性和对扰动的不敏感性.同时改进广义胞映射图论方法,提出盒子维数的广义胞映射图论方法的近似计算方法.展开更多
随着语义网络、社交网络、生物信息网络等新兴应用的涌现及普及,图数据的规模不断增大,针对大规模图数据的研究成为当今的研究热点和难点。可达查询是图数据处理中频繁使用的基础性查询,一些复杂的查询能够分解成包含多个可达查询的操...随着语义网络、社交网络、生物信息网络等新兴应用的涌现及普及,图数据的规模不断增大,针对大规模图数据的研究成为当今的研究热点和难点。可达查询是图数据处理中频繁使用的基础性查询,一些复杂的查询能够分解成包含多个可达查询的操作集合,其高效处理具有重要意义。针对大规模图的可达查询,提出了一种基于平面图覆盖的大规模图可达查询处理方法。首先给出了一种基于平面图覆盖的可达标签索引方法(planar graph cover based reachability labeling index method,PGCL)。该方法将最优树作为预处理应用于平面图覆盖,通过最优树创建、最优树分解以及树分解平面化处理,得到有向无环图(directed acyclic graph,DAG)的平面图覆盖,最大限度地保留了原图的可达性信息,从而基于覆盖顶点创建二维标签,用于压缩可达传递闭包。设计了基于PGCL的可达查询算法,有效实现了大规模图的可达查询。通过大量实验证明了提出的查询方法在保证查询的高效性情况下,更好地压缩了传递闭包,提高了可达查询的处理效率。展开更多
Appropriate maintenance technologies that facilitate model consistency in distributed simulation systems are relevant but generally unavailable.To resolve this problem,we analyze the main factors that cause model inco...Appropriate maintenance technologies that facilitate model consistency in distributed simulation systems are relevant but generally unavailable.To resolve this problem,we analyze the main factors that cause model inconsistency.The analysis methods used for traditional distributed simulations are mostly empirical and qualitative,and disregard the dynamic characteristics of factor evolution in model operational running.Furthermore,distributed simulation applications(DSAs)are rapidly evolving in terms of large-scale,distributed,service-oriented,compositional,and dynamic features.Such developments present difficulty in the use of traditional analysis methods in DSAs,for the analysis of factorial effects on simulation models.To solve these problems,we construct a dynamic evolution mechanism of model consistency,called the connected model hyper-digraph(CMH).CMH is developed using formal methods that accurately specify the evolutional processes and activities of models(i.e.,self-evolution,interoperability,compositionality,and authenticity).We also develop an algorithm of model consistency evolution(AMCE)based on CMH to quantitatively and dynamically evaluate influencing factors.Experimental results demonstrate that non-combination(33.7%on average)is the most influential factor,non-single-directed understanding(26.6%)is the second most influential,and non-double-directed understanding(5.0%)is the least influential.Unlike previous analysis methods,AMCE provides good feasibility and effectiveness.This research can serve as guidance for designers of consistency maintenance technologies toward achieving a high level of consistency in future DSAs.展开更多
运用广义胞映射图方法研究两个周期激励作用下Duffing-van der Pol系统的全局特性.发现了系统的混沌瞬态以及两种不同形式的瞬态边界激变,揭示了吸引域和边界不连续变化的原因.瞬态边界激变是由吸引域内部或边界上的混沌鞍和分形边界上...运用广义胞映射图方法研究两个周期激励作用下Duffing-van der Pol系统的全局特性.发现了系统的混沌瞬态以及两种不同形式的瞬态边界激变,揭示了吸引域和边界不连续变化的原因.瞬态边界激变是由吸引域内部或边界上的混沌鞍和分形边界上周期鞍的稳定流形碰撞产生.第一种瞬态边界激变导致吸引域突然变小,吸引域边界突然变大;第二种瞬态边界激变使两个不同的吸引域边界合并成一体.此外,在瞬态合并激变中两个混沌鞍发生合并,最后系统的混沌瞬态在内部激变中消失.这些广义激变现象对混沌瞬态的研究具有重要意义.展开更多
Crisis and stochastic bifurcation of the hardening Helmholtz-Duffing oscillator are studied by means of the generalized cell mapping method using digraph.For the system subject to a single deterministic harmonic excit...Crisis and stochastic bifurcation of the hardening Helmholtz-Duffing oscillator are studied by means of the generalized cell mapping method using digraph.For the system subject to a single deterministic harmonic excitation,our study reveals that a series of crisis phenomena can occur when the system parameter passes through different critical values,including chaotic boundary crisis,regular boundary crisis and interior crisis.A chaotic boundary crisis due to the collision of regular attractor with chaotic saddle embedded in a fractal basin boundary and an interior crisis due to the collision of regular attractor with chaotic saddle of its attraction basin are discovered.A new phenomenon,namely the global properties of dynamical system show symmetric as system parameter is varied,can be also revealed according to our analysis.For the system subject to a combination of a deterministic harmonic excitation and a random excitation,it is found that stochastic bifurcation,defined as a sudden change in character of a stochastic attractor,can occur one after another when the noise intensity passes through different critical values.This kind of stochastic bifurcation corresponds to stochastic crisis essentially.Our study also reveals that the generalized cell mapping method using digraph is a powerful tool not only for the crisis behavior analysis of deterministic system,but also for the global property analysis of stochastic bifurcation.展开更多
文摘应用广义胞映射图论方法(GCMD)研究SD(smooth and discontinuous systems)振子的内部激变现象.通过对SD常微分方程系统的全局分析发现周期解通向混沌的内部激变现象是由于周期吸引子与在其吸引域内部的混沌鞍碰撞产生的.混沌鞍是胞空间中的瞬态自循环胞集,周期吸引子与混沌鞍发生碰撞后,混沌鞍转化为混沌吸引子新增的一部分;内部激变不会改变原来吸引域的形状且具有可逆性和对扰动的不敏感性.同时改进广义胞映射图论方法,提出盒子维数的广义胞映射图论方法的近似计算方法.
文摘随着语义网络、社交网络、生物信息网络等新兴应用的涌现及普及,图数据的规模不断增大,针对大规模图数据的研究成为当今的研究热点和难点。可达查询是图数据处理中频繁使用的基础性查询,一些复杂的查询能够分解成包含多个可达查询的操作集合,其高效处理具有重要意义。针对大规模图的可达查询,提出了一种基于平面图覆盖的大规模图可达查询处理方法。首先给出了一种基于平面图覆盖的可达标签索引方法(planar graph cover based reachability labeling index method,PGCL)。该方法将最优树作为预处理应用于平面图覆盖,通过最优树创建、最优树分解以及树分解平面化处理,得到有向无环图(directed acyclic graph,DAG)的平面图覆盖,最大限度地保留了原图的可达性信息,从而基于覆盖顶点创建二维标签,用于压缩可达传递闭包。设计了基于PGCL的可达查询算法,有效实现了大规模图的可达查询。通过大量实验证明了提出的查询方法在保证查询的高效性情况下,更好地压缩了传递闭包,提高了可达查询的处理效率。
基金Project supported by the National Natural Science Foundation of China(No.61272336)
文摘Appropriate maintenance technologies that facilitate model consistency in distributed simulation systems are relevant but generally unavailable.To resolve this problem,we analyze the main factors that cause model inconsistency.The analysis methods used for traditional distributed simulations are mostly empirical and qualitative,and disregard the dynamic characteristics of factor evolution in model operational running.Furthermore,distributed simulation applications(DSAs)are rapidly evolving in terms of large-scale,distributed,service-oriented,compositional,and dynamic features.Such developments present difficulty in the use of traditional analysis methods in DSAs,for the analysis of factorial effects on simulation models.To solve these problems,we construct a dynamic evolution mechanism of model consistency,called the connected model hyper-digraph(CMH).CMH is developed using formal methods that accurately specify the evolutional processes and activities of models(i.e.,self-evolution,interoperability,compositionality,and authenticity).We also develop an algorithm of model consistency evolution(AMCE)based on CMH to quantitatively and dynamically evaluate influencing factors.Experimental results demonstrate that non-combination(33.7%on average)is the most influential factor,non-single-directed understanding(26.6%)is the second most influential,and non-double-directed understanding(5.0%)is the least influential.Unlike previous analysis methods,AMCE provides good feasibility and effectiveness.This research can serve as guidance for designers of consistency maintenance technologies toward achieving a high level of consistency in future DSAs.
文摘运用广义胞映射图方法研究两个周期激励作用下Duffing-van der Pol系统的全局特性.发现了系统的混沌瞬态以及两种不同形式的瞬态边界激变,揭示了吸引域和边界不连续变化的原因.瞬态边界激变是由吸引域内部或边界上的混沌鞍和分形边界上周期鞍的稳定流形碰撞产生.第一种瞬态边界激变导致吸引域突然变小,吸引域边界突然变大;第二种瞬态边界激变使两个不同的吸引域边界合并成一体.此外,在瞬态合并激变中两个混沌鞍发生合并,最后系统的混沌瞬态在内部激变中消失.这些广义激变现象对混沌瞬态的研究具有重要意义.
基金supported by the National Natural Science Foundation of China (Grant No.10872165)
文摘Crisis and stochastic bifurcation of the hardening Helmholtz-Duffing oscillator are studied by means of the generalized cell mapping method using digraph.For the system subject to a single deterministic harmonic excitation,our study reveals that a series of crisis phenomena can occur when the system parameter passes through different critical values,including chaotic boundary crisis,regular boundary crisis and interior crisis.A chaotic boundary crisis due to the collision of regular attractor with chaotic saddle embedded in a fractal basin boundary and an interior crisis due to the collision of regular attractor with chaotic saddle of its attraction basin are discovered.A new phenomenon,namely the global properties of dynamical system show symmetric as system parameter is varied,can be also revealed according to our analysis.For the system subject to a combination of a deterministic harmonic excitation and a random excitation,it is found that stochastic bifurcation,defined as a sudden change in character of a stochastic attractor,can occur one after another when the noise intensity passes through different critical values.This kind of stochastic bifurcation corresponds to stochastic crisis essentially.Our study also reveals that the generalized cell mapping method using digraph is a powerful tool not only for the crisis behavior analysis of deterministic system,but also for the global property analysis of stochastic bifurcation.
