耦合非线性振子：近似有效方程振幅分布的变态-1：3共振的情况

异向旋转耦合振子混合同步的实验实现

Experimental realization of mixed-synchronization in counter-rotating coupled oscillators

最近，在反转非线性耦合振子中观察到了一种新的混合同步现象。在混合同步状态下：一些变量是同相同步的，而另一些是异相同步的。实验验证了耦合反向旋转分段Rossler混沌振子中混合同步态的出现。近似稳定性分析的分析讨论和实验观察到的行为的数值验证。

外加强迫下全局耦合电化学振荡器的共振群聚

Resonance Clustering in Globally Coupled Electrochemical Oscillators with External Forcing

实验进行了全球耦合，外部强制人口的极限环电化学振荡器的近似单峰分布的异质性。全局耦合诱导相互夹带（在频率$ω_{1}$）状态;周期性强迫产生强制夹带（$ω_{\mathrm{F}}$）状态。由于相互夹带和强制夹带的相互作用，共振团簇状态以具有遵循共振规则$ω_{n}\cong nω_{1}-(n-1)ω_{\mathrm{F}}$的离散频率的频率的相等间隔发生。共振聚类需要一个最佳的，中间的全球耦合强度;在弱耦合的集群有较小的尺寸，并不严格遵循共振规则，而在强耦合的人口行为类似于一个单一的，巨大的振荡器。

Nonreciprocal wave scattering on nonlinear string-coupled oscillators

We study scattering of a periodic wave in a string on two lumped oscillators attached to it. The equations can be represented as a driven (by the incident wave) dissipative (due to radiation losses) system of delay differential equations of neutral type. Nonlinearity of oscillators makes the scattering non-reciprocal: the same wave is transmitted differently in two directions. Periodic regimes of scattering are analysed approximately, using amplitude equation approach. We show that this setup can act as a nonreciprocal modulator via Hopf bifurcations of the steady solutions. Numerical simulati…

Driven power-law oscillator

We explore the nonlinear dynamics of a driven power law oscillator whose shape varies periodically in time covering a broad spectrum of anharmonicities. Combining weak and strong confinement of different geometry within a single driving period the phase space allows not only for regular and chaotic bounded motion but in particular also for an unbounded motion which exhibits an exponential net growth of the corresponding energies. Our computational study shows that phases of motion with energy gain and loss as well as approximate energy conservation alternate within a single period of the oscil…

Nonlinear argumental oscillators: Stability criterion and attractor's capture probability

The behaviour of a space-modulated, so-called "argumental" oscillator is studied, which is represented by a model having an even-parity space-modulating function. Analytic expressions of a stability criterion and of discrete energy levels are given. Using an integrating factor and a Van der Pol representation in the (amplitude, phase) space, an approximate implicit closed-form of the solution is given. The probability to enter a stable-oscillation regime from given initial conditions is calculated in symbolic form. These results allow an analytic approach to stability and bifurcations of the s…

经典振子链的多体符号动力学

Many-body symbolic dynamics of a classical oscillator chain

我们研究了一类著名的Fermi-Pasta-Ulam粒子链，即粒子间势为四次双势阱的倒FPU模型。数值证据支持一个简单的符号描述的动态（在政权之间的井足够高的势垒）的（近似）马尔可夫过程。相应的转移矩阵形式上等同于具有长程耦合的铁磁海森堡量子自旋-1/2链，其对角化产生了模型的一类时间关联函数的精确估计。

Comparative Study of Homotopy Analysis and Renormalization Group Methods on Rayleigh and Van der Pol Equations

A comparative study of the Homotopy Analysis method and an improved Renormalization Group method is presented in the context of the Rayleigh and the Van der Pol equations. Efficient approximate formulae as functions of the nonlinearity parameter $\varepsilon$ for the amplitudes $a(\varepsilon)$ of the limit cycles for both these oscillators are derived. The improvement in the Renormalization group analysis is achieved by invoking the idea of nonlinear time that should have significance in a nonlinear system. Good approximate plots of limit cycles of the concerned oscillators are also presented…

时滞耦合时滞振子网络的稳定性

Stability of networks of delay-coupled delay oscillators

具有时滞的动态网络对数学分析提出了相当大的挑战。在这里，我们扩展了广义建模的方法来研究大型网络的延迟耦合延迟振荡器的稳定性。当网络的局部动态稳定性被绘制为两个延迟的函数时，就会发现一种舌状图案。利用结构和动力学之间的联系，我们确定的条件下，扰动的拓扑结构的稳定性有很大的影响。如果避开这些临界区域，大型随机网络的局部稳定性可以很好地近似解析。

Dynamics of two populations of phase oscillators with different frequency distributions

A large variety of rhythms are observed in nature. Rhythms such as electroencephalogram signals in the brain can often be regarded as interacting. In this study, we investigate the dynamical properties of rhythmic systems in two populations of phase oscillators with different frequency distributions. We assume that the average frequency ratio between two populations closely approximates some small integer. Most importantly, we adopt a specific coupling function derived from phase reduction theory. Under some additional assumptions, the system of two populations of coupled phase oscillators red…