周期轨道

参数X射线辐射与旋转周期轨道的局域分叉

The Parametric X-ray Radiation and Local Bifurcation in Rotated Periodic Orbit System

任何一点的ω-极限点或是f的一个周期轨道或者不包含f的周期轨道。

ω - limit set of every point is a periodic orbit of f or contains no periodic orbit of f.

给定能量的N体型问题多个几何上不同的周期轨道的存在性

The Existence of Multiple Geometrically Distinct Preiodic Orbits with Prescribed Energy for N-Body-Type Problems

一维Logistic映射稳定周期轨道存在的参数区域

1-dimensional Logistic Map Stable Periodic Orbits Existing Parameter Region

对混沌系统不稳定周期轨道（unstableperiodicorbits，UPO's）的搜索算法进行了深入研究。

The algorithms for searching unstable periodic orbits ( UPO 's ) of chaotic systems are studied .

关于Banach空间中连续自映射周期轨道存在问题

A Problem on the Existence of Periodic Orbit of Continuous Map in Banach Space

具收获与投放的三种群Volterra模型的周期轨道

Periodic orbits on three dimensional Volterra model with harvesting and stocking

离散型具有时滞复Volterra方程出现4-周期轨道解的条件

Condition for 4-Period Orbit Solution Occurrence in Discrete Complex Volterra Equation with Delay

数值模拟进一步验证了这种反馈控制方法可成功将Liu系统混沌运动轨道镇定到不稳定平衡点或不稳定周期轨道，即极限环上。

Numerical simulations show that the method can both suppress chaos to unstable equilibrium points and unstable periodic orbits ( limit cycles ) successfully .

在不连续映象系统中，一般一个周期轨道经由V型阵发失稳之后必须经过一系列过渡的高周期轨道才能过渡到混沌运动。

In discontinuous maps , in general a periodic orbit , after losing its stability , can transmit to chaos only via a sequence of high-period transition orbits .

结论非稳定周期轨道可以刻划HRV的动力学性质，是分析HRV的潜在的方法。

Conclusion UPOs can be used to characterize the dynamics of HRV and is a potential method to analyze HRV .

构造了Liapunov旋转函数V，利用旋转函数V，对非线性力学的三维动力系统周期轨道的最小周期作出了估计。

An estimate inequality for minimal period of the periodic orbits is given to a three-dimen-sional dynamical system in nonlinear mechanics by using Liapunov rotating function .

结果显示，当选取适当控制调节因子和控制参量，就可获得稳定不动点和不同nP周期轨道的控制结果。

The results show that the fixed point and the different np periodic orbit can be obtained by selecting proper control factors and parameters .

基于Lyapunov稳定性理论，设计了控制器，实现了快速跟踪混沌系统的不稳定周期轨道。

A controller is designed based on Lyapunov stability theory , and an unstable periodic orbit ( UPO ) tracking of uncertain chaotic systems is considered .

数值模拟结果表明，只要最大Lyapunov指数小于零，不同的s-波散射长度对应不同的周期轨道。

Numerical simulation shows that there are different periodic orbits according to different s-wave scattering length only if the maximal Lyapunov exponent of the system is negative .

本文证明：若f的扩张常数λ≥λm，k，则f有超旋转对为（k，km+1）的周期轨道。

In this paper , the authors prove that if f has an expanding constant λ≥λ, k , then it has a periodic orbit with over-rotation pair ( k , km + 1 ) .

根据这些参数向量下动力系统中吸引周期轨道的吸引域，构造出饰带群广义充满Julia集。

The filled-in Julia sets with the symmetry of frieze group are constructed based on the attracting fields of dynamical system with these parameter vectors .

利用OGY方法必须预先知道系统要被稳定的周期轨道，并且这种方法控制的实时性较差。

But the periodic orbit of the system must be found , before OGY method can work .

理论分析表明，稳定的周期轨道被嵌在Melnikov混沌吸引子中。

A theoretical analysis reveals that the stable periodic orbits are embedded in the Melnikov chaotic attractors .

从几何角度出发，参照系统慢流形选择控制参数，就能将vanderpol系统控制到指定的平衡态或振荡周期轨道上。

Based on its slow manifold to select control parameters , the slow-fast Van der Pol system can be controlled in predetermined equilibrium states or cyclical trajectories .

为刻划心脏节律存在的确定性动力学特征，运用不稳定周期轨道分析方法对健康青年人的RR间期时间序列数据进行分析。

To characterize the deterministic dynamics in heart rhythm , the unstable periodic orbit analysis were the RR interval time series of healthy young men .

通过分岔图来选择适当的控制参数，利用耦合反馈控制和xx控制两种控制方法将系统的混沌行为有效地控制到不同的周期轨道。

The proper controlling parameter can be selected via the bifurcation graph . The chaotic behaviors in the system can be effectively controlled to the different periodic orbits using the coupling feedback controlling and x | x | controlling methods .

计算并建立了次谐周期轨道的Melnikov函数，给出了Poincare映射出现周期m点的判据。

The Melnikov function of subharmonic orbits is calculated and established and the criterion of appearing periodical m point of Poincare mapping is presented .

该方法利用离散混沌系统的N步延时输出来估计系统的不稳定N周期轨道，并作为跟踪目标，使受控混沌系统既能稳定到相空间的确定点，又能稳定到N周期轨道。

Such control approach that uses the step-N delayed output of a chaotic system to estimate the unstable period-N orbit and to be the tracking target can stabilize a controlled chaotic system onto a deterministic point in the phase space as well as a period-N orbit .

通过对动力方程的分析求解，求出了系统的次谐周期轨道及其Melnikov函数，得到了方程存在次谐共振的条件。

The conditions for subharmonic resonance to exist were obtained , and the subharmonic periodic orbits of the system and their Melnikov functions were derived .

此外，还指出，当1<λ<λm，k时，在区间上存在单峰扩张自映射具有扩张常数λ却无超旋转对为（k，km+1）的周期轨道。

Besides , the authors show that there exists a unimodal expanding self-map of the interval which has an expanding constant A but no periodic orbit with over rotation pair ( k , mk + 1 ) if 1 < λ < λ m , k.

测试具有D4对称特性的平面排列动力系统的周期轨道，可以发现广义M集周期区域对充满Julia集中周期轨道的影响规律。

Testing the plane-tiling dynamics systems with D_4 symmetry , the affecting rules between period areas of general M sets and period orbits in filled-in Julia sets can be understood .

用Matlab进行数值仿真，调节延迟时间τ和控制增益k，DDFC系统能自动寻找和稳定不同的不稳定周期轨道UPO，实现混沌控制。

The UPOs ( unstable periodic orbits ) are found and stabilized by adjusting the gain k and delayed time τ in numerical simulations in Matlab . The control of chaos is realized .

首光找出Duffing方程的失稳周期轨道，然后通过连续追踪控制方法控制住了分岔区及混沌区中的失稳周期轨道。

In this paper , we firstly find out the unstable periodic orbit of Duffing equation , then control the unstable periodic orbit in bifurcation and chaotic regions by continuous tracing control method .

而某些探测任务，探测器定位在共线平动点附近的条件拟周期轨道（对应Lissajous轨道）上亦可以。

For some missions , requirements can be met to position an explorer in the conditional quasi-periodic orbits ( Lissajous Orbits ) around the collinear libration points .