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
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
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
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.
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.
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.
