Related papers: Stable fixed points in the Kuramoto model
The renormalisation group running of fermion mixing matrices in the Standard model and beyond is studied. For the massless 1-loop running with three generations six fixed points are found. Their associated anomalous dimension matrices are…
We study general properties of attractors for scalar-field dark energy scenarios which possess cosmological scaling solutions. In all such models there exists a scalar-field dominant solution with an energy fraction \Omega_{\phi}=1 together…
The Kuramoto model is a classical mathematical model in the field of non-linear dynamical systems that describes the evolution of coupled oscillators in a network that may reach a synchronous state. The relationship between the network's…
An interesting problem in synchronization is the study of coupled oscillators, wherein oscillators with different natural frequencies synchronize to a common frequency and equilibrium phase difference. In this paper, we investigate the…
We consider the existence of non-synchronized fixed points to the Kuramoto model defined on sparse networks: specifically, networks where each vertex has degree exactly three. We show that "most" such networks support multiple attracting…
We present the global-in-time existence of strong solutions and its large-time behavior for the Kuramoto-Sakaguchi equation with inertia. The equation describes the evolution of the probability density function for a large ensemble of…
We prove that a random group has fixed points when it isometrically acts on a CAT(0) cube complex. We do not assume that the action is simplicial.
By iterative techniques,we present two fixed point theorems, whose modular formulations are relatively close to the Banach's fixed point theorem in the normed spaces.The first result concerns the fixed point of the strongly contraction…
Kuramoto model is one of the most prominent models for the synchronization of coupled oscillators. It has long been a research hotspot to understand how natural frequencies, the interaction between oscillators, and network topology…
We propose a graphical notation by which certain spectral properties of complex systems can be rewritten concisely and interpreted topologically. Applying this notation to analyze the stability of a class of networks of coupled dynamical…
We are dealing with the question whether every group or semigroup action (with some additional property) on a continuum (with some additional property) has a fixed point. One of such results was given in 2009 by Shi and Sun. They proved…
Completely positive trace-preserving maps $S$, also known as quantum channels, arise in quantum physics as a description of how the density operator $\rho$ of a system changes in a given time interval, allowing not only for unitary…
We prove a fixed point theorem for the action of certain local monodromy groups on \'etale covers and use it to deduce lower bounds in essential dimension. In particular, we give more geometric proofs of many (but not all) of the results of…
In the Kuramoto model of globally coupled oscillators, partially locked states (PLS) are stationary solutions that incorporate the emergence of partial synchrony when the interaction strength increases. While PLS have long been considered,…
The existence and uniqueness of the common fixed point for generalized contractive mappings in order partial metric spaces is investigated. The existence of nonnegative solution of implicit nonlinear integral equations is also studied. Some…
Networks of coupled neural systems represent an important class of models in computational neuroscience. In some applications it is required that equilibrium points in these networks remain stable under parameter variations. Here we present…
The absolute sets of local systems on a smooth complex algebraic variety are the subject of a conjecture of N. Budur and B. Wang based on an analogy with special subvarieties of Shimura varieties. An absolute set should be the…
We establish an approximate fixed point result for self-maps on compact convex subsets of Hausdorff topological vector spaces where continuity is not a necessary condition.
Using the setting of $G$-metric spaces, common fixed point theorems for four maps satisfying the weakly commuting conditions are obtained for various generalized contractive conditions. Several examples are also presented to show the…
In this article, we derive a common fixed point result for a pair of single valued and set-valued mappings on a metric space having graphical structure. In this case, the set-valued map is assumed to be closed valued instead of closed and…