Related papers: On the flips for a synchronized system
Synchronization in a lattice of a finite population of phase oscillators with algebraically decaying, non-normalized coupling is studied by numerical simulations. A critical level of decay is found, below which full locking takes place if…
We investigate the minimal Hilbert-space dimension for a system to be synchronized. We first show that qubits cannot be synchronized due to the lack of a limit cycle. Moving to larger spin values, we demonstrate that a single spin 1 can be…
Short nonstandard proofs are given for some results about infinite systems of equations in infinitely many variables.
In this note, we give an alternative proof of the following result. Let p, q >= 2 be two multiplicatively independent integers. If an infinite set of integers is both p- and q-recognizable, then it is syndetic. Notice that this result is…
The asynchronous systems $f$ are the models of the asynchronous circuits from digital electrical engineering. They are multi-valued functions that associate to each input $u:\mathbf{R}\to \{0,1\}^{m}$ a set of states $x\in f(u),$ where…
A profinite group equipped with an expansive endomorphism is equivalent to a one-sided group shift. We show that these groups have a very restricted structure. More precisely, we show that any such group can be decomposed into a finite…
We investigate the universality of multi-spin systems in architectures of various symmetries of coupling type and topology. Explicit reachability sets under symmetry constraints are provided. Thus for a given (possibly symmetric)…
We look at spaces of infinite-by-infinite matrices, and consider closed subsets that are stable under simultaneous row and column operations. We prove that up to symmetry, any of these closed subsets is defined by finitely many equations.
We consider complete synchronization of identical maps coupled through a general interaction function and in a general network topology where the edges may be directed and may carry both positive and negative weights. We define mixed…
We consider linear iterated function systems (IFS) with a constant contraction ratio in the plane for which the "overlap set" $\Ok$ is finite, and which are "invertible" on the attractor $A$, the sense that there is a continuous surjection…
We prove that the non-separating curve complex of every surface of finite type and genus at least three admits an exhaustion by finite rigid sets.
Finite groups are of the greatest importance in science. Loops are a simple generalization of finite groups: they share all the group axioms except for the requirement that the binary operation be associative. The least loops that are not…
The emergence of synchronization in a network of coupled oscillators is a fascinating topic in various scientific disciplines. A coupled oscillator network is characterized by a population of heterogeneous oscillators and a graph describing…
The motion of a spinning football brings forth the possible existence of a whole class of finite dynamical systems where there may be non-denumerably infinite number of fixed points. They defy the very traditional meaning of the fixed point…
We prove that for every planar differential system with a period annulus there exists an involution $\sigma$ such that the system is $\sigma$-symmetric. We also prove that for for every planar differential system with a period annulus there…
In this paper we study the number of finite topologies on an $n$-element set subject to various restrictions.
Effects of synchronization in a system of two coupled oscillators with time-delayed feedback are investigated. Phase space of a system with time delay is infinite-dimensional. Thus, the picture of synchronization in such systems acquires…
Plane perfect matchings of $2n$ points in convex position are in bijection with triangulations of convex polygons of size $n+2$. Edge flips are a classic operation to perform local changes both structures have in common. In this work, we…
We provide a simple proof for a complementary pair of group codes over a finite non-commutative Frobenius ring of the fact that one of them is equivalent to the other one. We also explore this fact for checkeable codes over the same type of…
Let $(X,\Delta)$ be a log canonical $4$-fold over an algebraically closed field of characteristic zero. We prove that any sequence of $(K_X+\Delta)$-flips terminates.