相关论文: A toric deformation method for solving Kuramoto eq…
The production process of integrated electronic circuitry inherently leads to large heterogeneities on the component level. For electronic clock networks this implies detuned intrinsic frequencies and differences in coupling strength and…
Finding equilibria of the finite size Kuramoto model amounts to solving a nonlinear system of equations, which is an important yet challenging problem. We translate this into an algebraic geometry problem and use numerical methods to find…
In this paper, we develop a novel paradigm, namely hypergraph shift, to find robust graph modes by probabilistic voting strategy, which are semantically sound besides the self-cohesiveness requirement in forming graph modes. Unlike the…
The Kuramoto model of a network of coupled phase oscillators exhibits a first-order phase transition when the distribution of natural frequencies has a finite flat region at its maximum. First-order phase transitions including hysteresis…
Investigating the network stability or synchronization dynamics of multi-agent systems with time delays is of significant importance in numerous real-world applications. Such investigations often rely on solving the transcendental…
We propose a decomposition method for the spectral peaks in an observed frequency spectrum, which is efficiently acquired by utilizing the Fast Fourier Transform. In contrast to the traditional methods of waveform fitting on the spectrum,…
A noisy stabilized Kuramoto-Sivashinsky equation is analyzed by stochastic decomposition. For values of control parameter for which periodic stationary patterns exist, the dynamics can be decomposed into diffusive and transverse parts which…
In this paper, we study the deformation theory of degenerate algebraic curves on singular varieties which appear as the degenerate limit of families of varieties. For this purpose, we systematically develop a new method to calculate the…
Studying the landscape of nonconvex cost function is key towards a better understanding of optimization algorithms widely used in signal processing, statistics, and machine learning. Meanwhile, the famous Kuramoto model has been an…
Topological photonics holds the promise for enhanced robustness of light localization and propagation enabled by the global symmetries of the system. While traditional designs of topological structures rely on lattice symmetries, there is…
Synchronization is an omnipresent collective phenomenon in nature and technology, whose understanding is in particular for real-world systems still elusive. We study the synchronization transition in a phase oscillator system with two…
We study synchronization properties of systems of Kuramoto oscillators. The problem can also be understood as a question about the properties of an energy landscape created by a graph. More formally, let $G=(V,E)$ be a connected graph and…
The Candecomp/Parafac (CP) decomposition of the tensor whose maximal dimension is greater than its rank is considered. We derive the upper bound of rank under which the generic uniqueness of CP decomposition is guaranteed. The bound only…
In this paper has been considered probability-one global convergence of NFPH (Newton-Fixed Point Homotopy) algorithm for system of nonlinear equations and has been proposed a probability-one homotopy algorithm to solve a regularized…
The Kuramoto model is fundamental to the study of synchronization. It consists of a collection of oscillators with interactions given by a network, which we identify respectively with vertices and edges of a graph. In this paper, we show…
First order shape optimization methods, in general, require a large number of iterations until they reach a locally optimal design. While higher order methods can significantly reduce the number of iterations, they exhibit only local…
We study feedback control of the Kuramoto model with uniformly spaced natural frequencies defined on uniform graphs which may be complete, random dense or random sparse. The control objective is to drive all nodes to the same constant…
The phenomenon of synchronization occurs universally across the natural sciences and provides critical insight into the behavior of coupled nonlinear dynamical systems. It also offers a powerful approach to robust frequency or temporal…
In this paper gradient based topology optimization (TO) is used to discover 3-D phononic structures that exhibit ultra-wide normalized all-angle all-mode band gaps. The challenging computational task of repeated 3-D phononic band-structure…
This study extends the functional perturbation theory~(FPT) of dynamical systems, which was initially developed for investigating the shifts of magnetic field line trajectories within the chaotic edge region of plasma when subjected to…