集体相位灵敏度

全局耦合可兴奋元素的集体相位描述

Collective phase description of globally coupled excitable elements

本文提出全局耦合噪声可兴奋元素的集体相位描述理论，通过非线性Fokker-Planck方程推导集体相位方程，并证明集体相位灵敏度函数类型由分岔类型决定。

任意网络结构耦合振子的集体动力学响应

Collective dynamical response of coupled oscillators with any network structure

我们制定了一个减少理论，描述了作为一个整体的振荡器网络的外部强迫施加不均匀的组成振荡器的响应。本文还发展了弱耦合多振子网络的相位描述。给出了振荡器网络之间的集体相位灵敏度和有效相位耦合的一般公式，该理论适用于各种频率同步振荡器网络。任何网络结构都可以系统地对待。文中给出了几个例子来说明我们的理论。

Hopf-type neurons increase input-sensitivity by forming forcing-coupled ensembles

Astounding properties of biological sensors can often be mapped onto a dynamical system in the vicinity a bifurcation. For mammalian hearing, a Hopf bifurcation description has been shown to work across a whole range of scales, from individual hair bundles to whole regions of the cochlea. We reveal here the origin of this scale-invariance, from a general level, applicable to all neuronal dynamics in the vicinity of a Hopf bifurcation (embracing, e.g., Hodgkin-Huxley equations). When coupled by natural 'force-coupling', ensembles of Hopf oscillators below bifurcation threshold exhibit a collect…

Collective phase description of oscillatory convection

We formulate a theory for the collective phase description of oscillatory convection in Hele-Shaw cells. It enables us to describe the dynamics of the oscillatory convection by a single degree of freedom which we call the collective phase. The theory can be considered as a phase reduction method for limit-cycle solutions in infinite-dimensional dynamical systems, namely, stable time-periodic solutions to partial differential equations, representing the oscillatory convection. We derive the phase sensitivity function, which quantifies the phase response of the oscillatory convection to weak per…

集体振荡网络的相位-振幅约化与最优相位锁定

Phase-Amplitude Reduction and Optimal Phase Locking of Collectively Oscillating Networks

提出相位-振幅约化框架，分析网络化系统的集体振荡，捕捉偏离极限环的动力学，用于最优波形与反馈控制以实现快速相位锁定。

群体、相变和集体智慧

Swarms, Phase Transitions, and Collective Intelligence

提出了一个空间扩展模型的集体行为的大量的本地代理生物体中，生物体之间的移动概率在空间中的本地细胞，但与当地的形态发生物质，或morphogens依赖的权重。形态发生素又受到有机体传代的影响.形态发生物的进化和相应的生物流动构成了群体的集体行为。这种模型具有各种类型的相变和自组织特性，这些特性由噪声水平和其他参数控制。然后将该模型应用于蚂蚁在格子上移动的特定情况。蚂蚁的局部行为受到实验室中观察到的实际行为的启发，并且将集体行为的分析结果与相应的实验室结果进行比较。人们希望，目前的模式可以作为一个典型的例子，一个复杂的合作制度的性质。特别是群模型可以用来探索非平衡相变的关系，至少有三个重要的问题，在人工生命中遇到的。第一，作为复杂适应行为的涌现。第二，作为对生物系统中连续相变的探索。最后，推导出社会有机体中集体行为演化的行为准则。

Extracting phase coupling functions between collectively oscillating networks directly from time-series data

Many real-world systems are often regarded as weakly coupled limit-cycle oscillators, in which each oscillator corresponds to a dynamical system with many degrees of freedom that have collective oscillations. One of the most practical methods for investigating the synchronization properties of such a rhythmic system is to statistically extract phase coupling functions between limit-cycle oscillators directly from observed time-series data. In Particular, using a method that combines phase reduction theory and Bayesian inference, the phase coupling functions can be extracted from the time-serie…

American coot collective on-water dynamics

American coot (Fulica americana) flocks exhibit water surface (two-dimensional) collective dynamics that oscillate between two primary phases: a disordered phase of low density and non-uniform coot body orientations; a synchronized phase characterized by high density, uniform body orientations and speed. For this small-scale study, data was obtained for flocks of 10 to ~250 members for these phases. Approximate durations of phase occurrences were recorded for different flock sizes and for both relatively calm and severe weather conditions. Results indicate that for timed durations of up to ~ 2…

集体运动标量噪声模型（SNM）中连续相变的新情况

New aspects of the continuous phase transition in the scalar noise model (SNM) of collective motion

本文详细研究了集体运动标量噪声模型（SNM）中的相变性质。我们的结果证实了Vicsek等人的原始发现[Phys. Rev. Lett. 75（1995）1226]，SNM中的无序-有序转变对于小粒子速度（$v\leq 0.1$）是连续的二级相变。然而，对于大的速度（$v\geq 0.3$），我们发现一个强的各向异性的粒子扩散的各向同性扩散小的速度相比。各向异性扩散和周期性边界条件之间的相互作用导致人工对称破缺的解决方案（定向量子化密度波）和随之而来的一阶过渡一样的行为。因此，不可能得出关于SNM的大颗粒速度区域中的物理行为的任何结论。