随机系统鞍结分岔的无标度斑图

鞍结分岔附近弛豫轨线临界涨落的理论分析

Theoretical analysis for critical fluctuations of relaxation trajectory near a saddle-node bifurcation

研究了一个确定性部分发生鞍结分岔的Langevin方程。研究发现，在弱噪声极限下，系统的弛豫轨迹在鞍结分岔点附近具有发散特性，而确定性解的终值在该点处不连续变化.基于奇异摄动方法，建立了分析路径概率测度的系统公式。在这个公式中，批判的本质原来是源于从鞍点退出时间的中性。理论计算解释了数值模拟的结果。

跨临界、鞍结点和叉式离散与连续分岔中的普适有限时间标度

Universal finite-time scaling in the transcritical, saddle-node, and pitchfork discrete and continuous bifurcations

本文重新表述并扩展了动力系统接近分岔点时的有限时间标度律，将其推广至叉式等离散与连续分岔，并提出无需稳定不动点即可直接导出有限时间分岔图的普适方法。

When Hopf meets saddle: bifurcations in the diffusive Selkov model for glycolysis

We study the linear instabilities and bifurcations in the Selkov model for glycolysis with diffusion. We show that this model has a zero wave-vector, finite frequency Hopf bifurcation to a growing oscillatory but spatially homogeneous state and a saddle-node bifurcation to a growing inhomogeneous state with a steady pattern with a finite wavevector. We further demonstrate that by tuning the relative diffusivity of the two concentrations, it is possible to make both the instabilities to occur at the same point in the parameter space, leading to an unusual type of codimension-two bifurcation. We…

Reaction rates and the noisy saddle-node bifurcation: Renormalization group for barrier crossing

Barrier crossing calculations in chemical reaction-rate theory typically assume that the barrier is large compared to the temperature. When the barrier vanishes, however, there is a qualitative change in behavior. Instead of crossing a barrier, particles slide down a sloping potential. We formulate a renormalization group description of this noisy saddle-node transition. We derive the universal scaling behavior and corrections to scaling for the mean escape time in overdamped systems with arbitrary barrier height. We also develop an accurate approximation to the full distribution of barrier es…

二维变拓扑势场中的竞争隧穿轨道作为量子分岔模型

Competing tunneling trajectories in a 2D potential with variable topology as a model for quantum bifurcations

本文提出了一种处理二维量子分岔模型的路径积分方法.模型势有两个等效的极小值，由一个或两个鞍点分开，这取决于连续参数的值。因此，沿着一个轨迹或沿着两个等效路径实现调谐。零点波动模糊了这两个制度之间的急剧过渡，并导致一定的交叉行为。当两个鞍点不相等时，也可以有一个与两个轨迹中的一个变得不稳定的事实有关的一阶转变。我们说明了这些结果的数值调查。尽管这里研究的是一个特定的模型，但该方法是相当普遍的，并且对物理和化学中表现出多稳定性和隧穿现象的各种系统具有潜在的适用性。

非遍历跃迁动力学事件临界发散涨落理论

A theory for critically divergent fluctuations of dynamical events at non-ergodic transitions

本文从理论上研究了动力学事件在非遍历跃迁时的发散涨落。首先，我们发现非遍历跃迁可以被描述为时间关联函数的序参量的鞍连接分支。然后，遵循Ginzburg-Landau临界现象理论的基本思想，我们构造了一个唯象框架，利用这个框架我们可以确定鞍连接分岔点处的临界统计性质。采用这个框架，我们分析了一个模型，考虑的序参量的时空配置中的瞬子的波动。然后，我们得到的指数表征的长度尺度，时间尺度和序参量的波动幅度的发散鞍连接分歧。结果进行了比较与以前的研究的四点动态磁化率在非遍历转变的玻璃体系。