We study the Hamiltonian Mean Field (HMF) model of coupled Hamiltonian rotors with a heterogeneous distribution of moments of inertia and coupling strengths. We show that when the parameters of the rotors are heterogeneous, finite size fluctuations can greatly modify the coupling strength at which the incoherent state loses stability by inducing correlations between the momenta and parameters of the rotors. When the distribution of initial frequencies of the oscillators is sufficiently narrow, an analytical expression for the modification in critical coupling strength is obtained that confirms numerical simulations. We find that heterogeneity in the moments of inertia tends to stabilize the incoherent state, while heterogeneity in the coupling strengths tends to destabilize the incoherent state. Numerical simulations show that these effects disappear for a wide, bimodal frequency distribution.
Complex transitions to synchronization in delay-coupled networks of logistic maps
一个网络的延迟耦合逻辑映射表现出两种不同的同步制度，这取决于耦合延迟时间的分布。当延迟在整个网络中是均匀的时，网络将进入时间依赖状态[Atay et al.，物理修订信函92，144101（2004）]，根据延迟的不同，它可能是周期性的或混乱的;当延迟足够不均匀时，同步进入稳态，这对于非耦合映射来说是不稳定的[Masoller和Marti，Phys. Rev. Lett. 94，134102（2005）]。在这里，我们的特点的过渡依赖于时间的稳定状态的同步延迟分布的宽度增加。我们还比较了两个过渡到同步的耦合强度的增加。我们使用通过符号分析和有序模式计算的转移概率。我们发现，随着耦合强度的增加，在稳态同步开始之前，网络分裂成两个集群，这是在反相关系与对方。另一方面，随着延迟异质性的增加，没有团簇形成被认为是在稳态同步的开始，然而，一个相当复杂的非同步状态被检测到，揭示了在网络节点的转移概率的多样性。
