We investigate the effects of heterogeneous delays in the coupling of two excitable neural systems. Depending upon the coupling strengths and the time delays in the mutual and self-coupling, the compound system exhibits different types of synchronized oscillations of variable period. We analyze this synchronization based on the interplay of the different time delays and support the numerical results by analytical findings. In addition, we elaborate on bursting-like dynamics with two competing timescales on the basis of the autocorrelation function.
Vrije Universiteit Amsterdam（阿姆斯特丹自由大学）；Universität Hamburg（汉堡大学）；Saint Louis University（圣路易斯大学）；University of Oxford（牛津大学）；University of Exeter（埃克塞特大学）；Technische Universität München（慕尼黑工业大学）
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。
The problem of synchronization in heterogeneous networks of linear systems with nonlinear delayed diffusive coupling is considered. The network is presented in new coordinates mean-field dynamics and synchronization errors. Thus the problem of network synchronization is reduced to the studying of synchronization-error system stability. The circle criterion for time-delay systems is used to derive the stability conditions of synchronization-error system. Obtained results are applied to a network of neural mass model populations, and the synchronization conditions are established. Simulation res…
We study the synchronization of oscillators with inertias and phase shifts, namely the second-order Kuramoto-Sakaguchi model. Using the self-consistent method, we find that the effect of inertia is the introduction of effective phase shifts. The discontinuous synchronization transition of the Kuramoto-Sakaguchi model changes to a continuous one when the value of inertia is small. In addition, we find a new synchronization process, in which with increasing coupling strength the system reaches an oscillating state instead of complete synchronization due to the cross-effect of phase shifts and in…
We investigate the synchronization phenomenon between two Spin-transfer Torque Nano-Oscillators (STNOs) of different frequencies in two pillar systems under vortex configuration detunings or driving frequencies. The oscillators' mutual synchronization occurs through magnetic dipolar interaction. Our micromagnetic simulations show that an amplitude fluctuation referred to as $Γ_p$ has a significant impact on determining the synchronization frequency. The evolution of frequency and amplitude fluctuation rate in two different oscillator sizes versus external perpendicular field are compared and d…
Nonlocally coupled oscillators with a phase lag self-organize into various patterns such as global synchronization, the twisted state, and the chimera state. In this paper, we consider nonlocally coupled oscillators that move on a ring by randomly exchanging their positions with the neighbors, and investigate the combined effects of phase lag and mobility on the collective phase dynamics. Spanning the whole range of phase lag and mobility, we show that mobility promotes synchronization for an attractive coupling, while it destroys coherence for a repulsive coupling. The transition behaviors ar…
We numerically study the synchronization of an identical population of Kuramoto-Sakaguchi phase oscillators in Watts-Strogatz networks. We find that, unlike random networks, phase-shift could enhance the synchronization in small-world networks. We also observe abrupt phase transition with hysteresis at some values of phase shifts in small-world networks, signs of an explosive phase transition. Moreover, we report the emergence of Chimera states at some values of phase-shift close to the transition points, which consist of spatially coexisting synchronized and desynchronized domains.
We study synchronization in large populations of coupled phase oscillators with time-delays, higher order interactions. With each of these effects individually giving rise to bistabiltiy between incoherence and synchronization via a subcriticality at the onset of synchronization and the development of a saddle node, we find that their combination yields another mechanism behind bistability, where supercriticality at onset may be maintained and instead the formation of two saddle nodes creates tiered synchronization, i.e., bistability between a weakly synchronized state and a strongly synchroni…
We implement nonlinear anharmonic interaction in the coupled van der Pol oscillators to investigate the quantum synchronization behaviour of the systems. We study the quantum synchronization in two oscillator models, coupled quantum van der Pol oscillators and anharmonic self-oscillators. We demonstrate that the considered systems exhibit a high-order synchronization through coupling in both classical and quantum domains. We show that due to the anharmonicity of the nonlinear interaction between the oscillators the system exhibits phonon blockade in the phase locking regime which is a pure non…
