相关论文: Hyperbolic Geometry of Kuramoto Oscillator Network…
This paper is concerned with the existence of multiple stable fixed point solutions of the homogeneous Kuramoto model. We develop a necessary condition for the existence of stable fixed points for the general network Kuramoto model. This…
A Kuranishi space is a topological space with a Kuranishi structure, defined by Fukaya and Ono. Kuranishi structures occur naturally on moduli spaces of J-holomorphic curves in symplectic geometry. This paper is a brief introduction to the…
Networks of coupled dynamical units give rise to collective dynamics such as the synchronization of oscillators or neurons in the brain. The ability of the network to adapt coupling strengths between units in accordance with their activity…
Time-delayed oscillator networks underlie diverse biological and physical systems, yet standard first-order phase reductions fail to capture their high-dimensional collective dynamics. In this Letter, we develop a universal second-order…
We study 3D chaotic dynamics through an analysis of transport in a granular flow in a half-full spherical tumbler rotated sequentially about two orthogonal axes (a bi-axial "blinking" tumbler). The flow is essentially quasi-2D in any…
We present a novel geometric approach for determining the unique structure of a Hamiltonian and establishing an instability criterion for quantum quadratic systems. Our geometric criterion provides insights into the underlying geometric…
It has long been known that the moduli space of hyperbolic metrics on the disc can be identified with the Virasoro coadjoint orbit $\mathrm{Diff}^+(S^1) / \mathrm{SL}(2,\mathbb{R})$. The interest in this relationship has recently been…
We study nematic configurations within three-dimensional (3D) cuboids, with planar degenerate boundary conditions on the cuboid faces, in the Landau-de Gennes framework. There are two geometry-dependent variables: the edge length of the…
3D Loop Quantum Gravity with a vanishing cosmological constant can be related to the quantization of the $\textrm{SU}(2)$ BF theory discretized on a lattice. At the classical level, this discrete model characterizes discrete flat geometries…
The main purpose of this article is to study box dimension of orbits near hyperbolic and nonhyperbolic fixed points of discrete dynamical systems in higher dimensions. We generalize the known results for one-dimensional systems, that is,…
We study the global bifurcations of frequency weighted Kuramoto model in low-dimension for network of fully connected oscillators. To study the effect of non-zero-centered frequency distribution, we consider two symmetric Lorentzians as an…
We explore chaos in the Kuramoto model with multimodal distributions of the natural frequencies of oscillators and provide a comprehensive description under what conditions chaos occurs. For a natural frequency distribution with $M$ peaks…
We establish a unified synchronization framework for the all-to-all hybrid Kuramoto model that couples first- and second-order oscillators within a single dynamical system. Although the Kuramoto model has become one of the most widely used…
We study the deformation behavior of Kobayashi hyperbolic embeddings for complements of divisors in projective toric varieties. In the toric setting, entire curves in divisor complements propagate along algebraic subtori, allowing…
We extend the twisted gauge theory model of topological orders in three spatial dimensions to the case where the three spaces have two dimensional boundaries. We achieve this by systematically constructing the boundary Hamiltonians that are…
The classification of the unitary irreducible representations of symmetry groups is a cornerstone of modern quantum physics, as it provides the fundamental building blocks for constructing the Hilbert spaces of theories admitting these…
We consider the classical momentum- or velocity-dependent two-dimensional Hamiltonian given by $$\mathcal H_N = p_1^2 + p_2^2 +\sum_{n=1}^N \gamma_n(q_1 p_1 + q_2 p_2)^n ,$$ where $q_i$ and $p_i$ are generic canonical variables, $\gamma_n$…
We use the method of the exact renormalization group to study the renormalization group flows of an O(N) invariant Yukawa model in three dimensional Euclidean space consisting of one real scalar and N real spinor fields. We obtain a phase…
The existence of parabolic orbits is obtained for a class of singular Hamiltonian systems $\ddot{u}(t)+\nabla V(u(t))=0$ by taking limit for a sequence of non-collision periodic solutions which are obtained by Mountain Pass Lemma.
Certain systems of coupled identical oscillators like the Kuramoto-Sakaguchi or the active rotator model possess the remarkable property of being Watanabe-Strogatz integrable. We prove that such systems, which couple via a global order…