论文标题
具有cauchy噪声的双峰丘脑系统中对不对称性的同步过渡和敏感性
Synchronization transitions and sensitivity to asymmetry in the bimodal Kuramoto systems with Cauchy noise
论文作者
论文摘要
我们分析了在cauchy噪声强迫下，在两个分布组件之间的双峰分布和两个分布组件之间的双峰分布和两个分布之间的双峰分布下，热力学大型系统的热力学大型系统的同步动力学。带有Cauchy噪声的系统承认Ott-Antonsen Ansatz的应用，这使我们能够在对称和不对称病例中研究分析同步转变。 The dynamics and the transitions between various synchronous and asynchronous regimes are shown to be very sensitive to the asymmetry degree whereas the scenario of the symmetry breaking is universal and does not depend on the particular way to introduce asymmetry, be it the unequal populations of modes in bimodal distribution, the phase delay of the Kuramoto-Sakaguchi model, the different values of the coupling constants, or the两种模式的噪声水平不等。特别是，我们发现，即使是小的不对称性也可能稳定固定的部分同步状态，即使对于两种分布模式之间的任意频率差异（振荡器亚组），这也可能发生。这种效果还导致两个固定的部分同步状态之间的新型双匹配性：一种具有较高的全局同步和两个亚组之间的同步均衡性，而另一个具有较低同步的同步，其中一个亚组具有主导性，具有较高的内部（亚组）同步水平，并且在第二个子组上的振动频率较高。对于四种不对称类型，在分析上发现了不对称参数的临界值，在该值之上不再可能不连贯和部分同步状态之间的双稳定性。
We analyze the synchronization dynamics of the thermodynamically large systems of globally coupled phase oscillators under Cauchy noise forcings with bimodal distribution of frequencies and asymmetry between two distribution components. The systems with the Cauchy noise admit the application of the Ott-Antonsen ansatz, which has allowed us to study analytically synchronization transitions both in the symmetric and asymmetric cases. The dynamics and the transitions between various synchronous and asynchronous regimes are shown to be very sensitive to the asymmetry degree whereas the scenario of the symmetry breaking is universal and does not depend on the particular way to introduce asymmetry, be it the unequal populations of modes in bimodal distribution, the phase delay of the Kuramoto-Sakaguchi model, the different values of the coupling constants, or the unequal noise levels in two modes. In particular, we found that even small asymmetry may stabilize the stationary partially synchronized state, and this may happen even for arbitrarily large frequency difference between two distribution modes (oscillator subgroups). This effect also results in the new type of bistability between two stationary partially synchronized states: one with large level of global synchronization and synchronization parity between two subgroups and another with lower synchronization where the one subgroup is dominant, having higher internal (subgroup) synchronization level and enforcing its oscillation frequency on the second subgroup. For the four asymmetry types, the critical values of asymmetry parameters were found analytically above which the bistability between incoherent and partially synchronized states is no longer possible.
