Related papers: A Cyclic Small Phase Theorem
This paper introduce the notion of output contraction that expands the contraction notion to the time-varying nonlinear systems with output. It pertains to the systems' property that any pair of outputs from the system converge to each…
In this work, we study the phase estimation problem. We show an alternative, simpler and self-contained proof of query lower bounds. Technically, compared to the previous proofs [NW99, Bes05], our proof is considerably elementary.…
We discuss the nature of phase transitions in self-gravitating systems both in the microcanonical and in the canonical ensemble. We avoid the divergence of the gravitational potential at short distances by considering the case of…
We define an ensemble of random Clifford quantum circuits whose output state undergoes an entanglement phase transition between two volume-law phases as a function of measurement rate. Our setup maps exactly the output state to the ground…
Weakly coupled oscillators are used throughout the physical sciences, particularly in mathematical neuroscience to describe the interaction of neurons in the brain. Systems of weakly coupled oscillators have a well-known decomposition to a…
The topological theory of phase transitions was proposed on the basis of different arguments, the most important of which are: a direct evidence of the relation between topology and phase transitions for some exactly solvable models; an…
A method is given for generating a bounded invariant of a differential system with a given set of initial conditions around a point $x_0$. This invariant has the form of a tube centered on the Euler approximate solution starting at $x_0$,…
Multifractal analysis of stochastic processes deals with the fine scale properties of the sample paths and seeks for some global scaling property that would enable extracting the so-called spectrum of singularities. In this paper we…
The purpose of this article is to introduce the original results which devoted with the nonlinear control system problems involves of nonlinear differential equations of fractional orders. Thus, this system is described with a mixed of…
Recently, it has been proposed that exotic one-dimensional phases can be realized by gapping out the edge states of a fractional topological insulator. The low-energy edge degrees of freedom are described by a chain of coupled parafermions.…
An external description for nonperiodically sampled multivariable linear systems has been developed. Emphasis is on the sampling period sequence, included among the variables to be handled. The computational procedure is simple and no use…
We formulate and study the set of coupled nonlinear differential equations which define a series of shape invariant potentials which repeats after a cycle of $p$ iterations. These cyclic shape invariant potentials enlarge the limited…
A numerical technique used to solve boundary value problems is modified to find periodic steady-state solutions of nonautonomous dynamical systems. The technique uses a matrix representation of the time derivative obtained through…
In this paper, we study the maximum number of limit cycles for the piecewise smooth system of differential equations $\dot{x}=y, \ \dot{y}=-x-\varepsilon \cdot (f(x)\cdot y +{\rm sgn}(y)\cdot g(x))$. Using the averaging method, we were able…
This paper shows that a necessary and sufficient condition for the small-signal stability of an inverter-integrated power system can be expressed in terms of semidefinite matrix inequalities determined only by the synchronous reactance of…
The concept of topological phases has been generalized to higher-order topological insulators and superconductors with novel boundary states on corners or hinges. Meanwhile, recent experimental advances in controlling dissipation (such as…
In the analysis and control of discrete-time linear time-invariant systems, the spectral radius of the system state matrix plays an essential role. Usually, it is assumed that system matrices are known, from which the spectral radius can be…
Given a discrete-state continuous-time reactive system, like a digital circuit, the classical approach is to first model it as a state transition system and then prove its properties. Our contribution advocates a different approach: to…
Using a recently proposed classification scheme for phase transitions in finite systems [Phys.Rev.Lett.{\bf 84},3511 (2000)] we show that within the statistical standard model of nuclear multifragmentation the predicted phase transition is…
Definition of the phase of oscillations is straightforward for deterministic periodic processes but nontrivial for stochastic ones. Recently, Thomas and Lindner in [Phys. Rev. Lett., v. 113, 254101 (2014)] suggested to use the argument of…