A note concerning the 2:1 and the 3:2 resonances in the asteroid belt     

Jacques Henrard 《Celestial Mechanics and Dynamical Astronomy》1996,64(1-2):107-114

The dynamical behavior of asteroids inside the 2:1 and 3:2 commensurabilities with Jupiter presents a challenge. Indeed most of the studies, either analytical or numerical, point out that the two resonances have a very similar dynamical behavior. In spite of that, the 3:2 resonance, a little outside the main belt, hosts a family of asteroids, called the Hildas, while the 2:1, inside the main belt, is associated to a gap (the Hecuba gap) in the distribution of asteroids.In his search for a dynamical explanation for the Hecuba gap, Wisdom (1987) pointed out the existence of orbits starting with low eccentricity and inclination inside the 2:1 commensurability and going to high eccentricity, and thus to possible encounters with Mars. It has been shown later (Henrard et al.), that these orbits were following a path from the low eccentric belt of secondary resonances to the high eccentric domain of secular resonances. This path crosses a bridge, at moderate inclination and large amplitude of libration, between the two chaotic domains associated with these resonances.The 3:2 resonance being similar in many respects to the 2:1 resonance, one may wonder whether it contains also such a path. Indeed we have found that it exists and is very similar to the 2:1 one. This is the object of the present paper.  相似文献   

Frequency analysis of a dynamical system     

Jacques Laskar 《Celestial Mechanics and Dynamical Astronomy》1993,56(1-2):191-196

Frequency analysis is a new method for analyzing the stability of orbits in a conservative dynamical system. It was first devised in order to study the stability of the solar system (Laskar, Icarus, 88, 1990). It is a powerful method for analyzing weakly chaotic motion in hamiltonian systems or symplectic maps. For regular motions, it yields an analytical representation of the solutions. In cases of 2 degrees of freedom system with monotonous torsion, precise numerical criterions for the destruction of KAM tori can be found. For a 4D symplectic map, plotting the frequency map in the frequency plane provides a clear representation of the global dynamics and describes the actual Arnold web of the system.  相似文献   

Generalized Lyapunov exponents indicators in Hamiltonian dynamics: An application to a double star system     

E. Lohinger  C. Froeschlé  R. Dvorak 《Celestial Mechanics and Dynamical Astronomy》1993,56(1-2):315-322

The Lyapunov characteristic numbers (LCNs) which are defined as the mean value of the distribution of the local variations of the tangent vectors to the flow (=ln _k ⁱ ) (see Froeschlé, 1984) have been found to be sensitive indicators of stochasticity. So we computed the distribution of these local variations and determined the moments of higher order for the integrable and stochastic regions in a binary star system with =0.5.  相似文献   

Asteroid motion near the 3 : 1 resonance     

John D. Hadjidemetriou 《Celestial Mechanics and Dynamical Astronomy》1993,56(4):563-599

A mapping model is constructed to describe asteroid motion near the 3 : 1 mean motion resonance with Jupiter, in the plane. The topology of the phase space of this mapping coincides with that of the real system, which is considered to be the elliptic restricted three body problem with the Sun and Jupiter as primaries. This model is valid for all values of the eccentricity. This is achieved by the introduction of a correcting term to the averaged Hamiltonian which is valid for small values of the ecentricity.We start with a two dimensional mapping which represents the circular restricted three body problem. This provides the basic framework for the complete model, but cannot explain the generation of a gap in the distribution of the asteroids at this resonance. The next approximation is a four dimensional mapping, corresponding to the elliptic restricted problem. It is found that chaotic regions exist near the 3 : 1 resonance, due to the interaction between the two degrees of freedom, for initial conditions close to a critical curve of the circular model. As a consequence of the chaotic motion, the eccentricity of the asteroid jumps to high values and close encounters with Mars and even Earth may occur, thus generating a gap. It is found that the generation of chaos depends also on the phase (i.e. the angles andv) and as a consequence, there exist islands of ordered motion inside the sea of chaotic motion near the 3 : 1 resonance. Thus, the model of the elliptic restricted three body problem cannot explain completely the generation of a gap, although the density in the distribution of the asteroids will be much less than far from the resonance. Finally, we take into account the effect of the gravitational attraction of Saturn on Jupiter's orbit, and in particular the variation of the eccentricity and the argument of perihelion. This generates a mixing of the phases and as a consequence the whole phase space near the 3 : 1 resonance becomes chaotic. This chaotic zone is in good agreement with the observations.  相似文献   

基于混沌吸引子的复杂农业系统预测模型研究   总被引：1，自引：0，他引：1  

陈朝霞  周宏  余德贵 《南京气象学院学报》2004,27(6):862-866

农业生产是自然再生产和经济再生产有机结合的过程，农业系统是高度耦合了自然生态、社会经济系统等的复杂大系统，具有非线性和耗散性特征。复杂农业系统要素非线性作用所表现的系统行为形成农业系统的整个演化轨迹。从长期演化来看，由于系统内部自组织作用、系统协同和外部随机扰动的作用使得农业系统出现混沌现象，故复杂系统具有长期不可预测性。本文根据复杂农业系统的预测规范，重构复杂农业系统相空间，建立了基于“混沌吸引子”的非线性混沌动力学预测模型，并以成都的相关数据进行分析验证。  相似文献   

Persistent alternate abundance states in the coral reef sea urchin Diadema savignyi: evidence of alternate attractors          下载免费PDF全文

Xueying Han 《Marine Ecology》2016,37(6):1179-1189

Alternate attractors have been shown to exist in a variety of terrestrial and aquatic systems, e.g. temperate forests, savannas, shallow lakes, wetlands, coral reefs, kelp forests. The shift from one attractor to another, also referred to as a regime shift, is thought to occur when a system passes some critical threshold such that the trajectory of the system changes direction. Alternate attractors in population dynamics can also exist, leading to alternate stable states in the population abundance of a species. This study explored alternate attractors in the population dynamics of the Indo‐Pacific sea urchin Diadema savignyi and the potential underlying mechanisms that promote its bi‐stability. In Moorea, French Polynesia, the local abundance of D. savignyi, a functionally important herbivore in lagoon habitats, occurs in two states: (i) solitary individuals that occupy crevices in low densities and (ii) aggregations of tens to hundreds of individuals. These different states are temporally stable and are not explained by spatial differences in recruitment rates of juveniles. A field experiment revealed that the per capita mortality rate of adult D. savignyi was substantially lower at sites where urchins occurred in aggregations compared with sites at which they were solitary individuals. An additional experiment showed that per capita mortality decreased with increasing aggregation size. Individuals in high‐density aggregations, however, had significantly smaller test diameters than solitary individuals, indicating that individuals in aggregations may be food limited. Collectively, the evidence suggests that the two different local abundance states of D. savignyi result from negative feedback loops where high local density can be maintained by aggregative behavior that greatly reduces per capita risk of predation when the local number of adult sea urchins is sufficiently large; sites with few sea urchins remain at low density because individuals are more susceptible to predation when crevices are occupied but there are not enough individuals to form large aggregations. Thus, there may be alternate attractors in the population dynamics of D. savignyi that can produce either persistently low or high local population densities.  相似文献   

基于阈值可调切换系统的多翅膀混沌吸引子设计及电路仿真     

石擎宇  黄霞 《南京气象学院学报》2019,11(4):467-473

本文提出了一种通过调节一类状态依赖切换系统的阈值来生成多翅膀混沌吸引子的设计方案.首先,设计了两个类Lorenz子系统;然后,基于这两个子系统构造了一个状态依赖于阈值的切换策略,从而构造了一类状态依赖于阈值的切换系统;最后,通过调整切换系统的阈值来改变鞍焦平衡点的个数与分布,使得该切换系统能够产生4-6-8翅膀的混沌吸引子.此外,根据切换系统的状态方程设计了该系统的模拟电路,电路仿真结果与数值仿真结果一致.实验结果证实：该设计方案可以在不增加系统维数或无需设计复杂非线性函数的情况下生成多翅膀混沌吸引子.  相似文献   

A SPECTRUM OF LYAPUNOV EXPONENTS OBTAINED FROM A CHAOTIC TIME SERIES          下载免费PDF全文

Yan Shaojin  Peng Yongqing  Wang Jianzhong 《Acta Meteorologica Sinica》1992,6(3):379-385

A complete spectrum of Lyapunov exponents (LEs) is obtained from 1970— 1985 daily mean pressuremeasurements at Shanghai by means of a correlation matrix analysis technique and it is found that there exist LEs≥0,and <0. with their sum 0λ_i=K=0.110405 whereuponT=1 /K =9 is obtained as the predictable time scale, a result close to that acquired by the dynamic-statistical approachin early days and also in agreement with that present by the authors themselves(1991).  相似文献   

Wavelet analysis of the standard map: Structure and scaling     

A. D. Gilbert  C. Froeschlé  U. Frisch 《Celestial Mechanics and Dynamical Astronomy》1993,56(1-2):263-272

Wavelet analysis is applied to distributions of points generated by iterating the standard map. The initial condition is chosen so that the points fill the largest chaotic region. When the standard map parameterk=1.3, the distribution of points contains many voids corresponding to islands in the chaotic region. The wavelet transform is dominated by contributions from these islands. Fork=10 the chaos fills phase space and no structure is apparent; the wavelet transform reveals statistical fluctuations in the distribution of points.  相似文献   

区域旱涝气候混沌动力学可预报性研究   总被引：1，自引：0，他引：1       下载免费PDF全文

栗珂  郑小华  屈振江 《热带气象学报》2007,23(6):669-672

根据西安地区旱涝气候等级近1624a（380-2003年）资料序列，运用非线性系统混沌动力学理论，通过计算气候吸引子的关联维数、Kolmogorov熵和Lyapunov指数，对西安区域旱涝气候的混沌特性和可预报性进行研究。结果表明：西安区域旱涝气候系统是一个具有有限个自由度的复杂的混沌系统。其吸引子关联维数约为3．1，确定性的平均可预报时间尺度约为14．8a，最大可预报时间尺度约为20．7a。  相似文献