Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2104.05954

The lower bound of the network connectivity guaranteeing in-phase synchronization

Ryosuke Yoneda·Tsuyoshi Tatsukawa·Jun-nosuke Teramae
View original source ↗Read source document ↗Export metadata ↓

Abstract

In-phase synchronization is a stable state of identical Kuramoto oscillators coupled on a network with identical positive connections, regardless of network topology. However, this fact does not mean that the networks always synchronize in-phase because other attractors besides the stable state may exist. The critical connectivity $\mu_{\mathrm{c}}$ is defined as the network connectivity above which only the in-phase state is stable for all the networks. In other words, below $\mu_{\mathrm{c}}$, one can find at least one network which has a stable state besides the in-phase sync. The best known evaluation of the value so far is $0.6828\cdots\leq\mu_{\mathrm{c}}\leq0.75$. In this paper, focusing on the twisted states of the circulant networks, we provide a method to systematically analyze the linear stability of all possible twisted states on all possible circulant networks. This method using integer programming enables us to find the densest circulant network having a stable twisted state besides the in-phase sync, which breaks a record of the lower bound of the $\mu_{\mathrm{c}}$ from $0.6828\cdots$ to $0.6838\cdots$. We confirm the validity of the theory by numerical simulations of the networks not converging to the in-phase state.

Explore related subjects

nlin.AOnlin.CD

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Ryosuke Yoneda, Tsuyoshi Tatsukawa, Jun-nosuke Teramae. 2021-04-13. The lower bound of the network connectivity guaranteeing in-phase synchronization. https://doi.org/10.1063/5.0054271

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Reconstructing the information processing capacity of physical systems from noisy observations

Driven dynamical systems can compute when their transient states encode complex transformations of past inputs. The information processing capacity (IPC) framework allows for a detailed accounting of these computational properties, however its interpretation in noisy systems has remained incomplete. In this work, we clarify how noise affects the IPC and how one can reconstruct the noiseless IPC. First, we show how to distinguish the dynamics of an unperturbed system from the noise-free component of the stochastic dynamics: The IPC measured for responses averaged over noise realizations is in general not the same as the IPC of the unperturbed system. We explicitly demonstrate that noise can redistribute computational capacity and sometimes even enhance performance on particular tasks, rather than merely degrading a fixed computation. We then introduce covariance reconstruction by orthogonal projection (CROP), which reconstructs the covariance and IPC of the noise-free component directly from noisy observations, without requiring a detailed model of either the system or the noise. At fixed total measurement budget, numerical tests on a classical nonlinear reservoir show that CROP estimates the noise-free IPC more accurately than the standard practice of ensemble averaging over repeated trials. We find the same advantage in a quantum reservoir subject to unavoidable measurement noise. Our results provide a general route to recovering the computational structure of noisy physical systems from finite observations.

nlin.AO↗
arXiv2026

Double explosive transitions in adaptive multilayer networks with higher-order interactions

Can asymmetry between two interacting networks fundamentally change how they synchronize? We identify double explosive transitions in the forward direction, backward direction, or a combination thereof, with single or double hysteresis loops in an adaptive bilayer multiplex network of Kuramoto oscillators with pairwise and three-body interactions and asymmetric phase lags. Using the Ott-Antonsen reduction, we derive a low-dimensional system and perform a stability analysis. The reduced model accurately captures the full microscopic dynamics and enables analytical expressions for the bifurcation points. Systematic mapping across multiple parameter planes reveals eight distinct synchronization regimes. The relative ordering of saddle-node and pitchfork bifurcation points---controlled by phase-lag asymmetry, cross-layer adaptation, and the higher-order interaction strength---creates two distinct coherent branches (weak and strong), giving rise to double explosive transitions. Crucially, phase-lag asymmetry acts as a robust control knob: while symmetric phase lags suppress explosive transitions, layer-specific differences promote multistability and double explosive transitions. The higher-order interaction strength $K_2$ and adaptation strengths $q$, $p$, and $h$ further modulate these transitions in a complex, parameter-dependent manner. Excellent agreement between analytical predictions and numerical simulations confirms the robustness of our reduced description.

nlin.AO↗
arXiv2026

Spatio-temporal structures in frog chorus with two species examined by laboratory experiments and mathematical modeling

Synchronization can be observed in various systems in physics and biology. The choruses of male frogs are known as an example of biological synchronization in which the well-organized temporal structure, i.e., anti-phase synchronization between neighbors, is realized. Given that male frogs produce sounds to advertise their territories to competitors, the dynamics of phases and spatial coordinates should be mutually coupled in the frog choruses. In this study, we examined the spatio-temporal dynamics in the choruses consisting of male Japanese tree frogs and other acoustic animals. First, we carried out playback experiments using actual frogs and observed that male Japanese tree frog synchronized in anti-phase with the stimuli of a similar frequency but did not synchronize with the stimuli of a much different frequency. Second, we modeled the choruses with two species as a system of coupled mobile oscillators and numerically evaluated how the spatio-temporal structure depends on the similarity of call frequencies. Numerical simulations of the model showed that (1) the two-cluster antisynchronization is established in the same species when the distributions of call frequencies are much different between two species and (2) the two-cluster antisynchronization is disturbed when the distributions of call frequencies are similar. These results highlight the occurrence of various spatio-temporal patterns in the proposed model, indicating the importance of repulsive effects with different weights on the variation of the spatio-temporal patterns.

nlin.AO↗