Related papers: Amplitude bounds for biochemical oscillators

The quenching of oscillations in interacting systems leads to several unwanted situations, which necessitate a suitable remedy to overcome the quenching. In this connection, this work addresses a mechanism that can resurrect oscillations in…

Here we analytically examine the response of a limit cycle solution to a simple differential delay equation to a single pulse perturbation of the piecewise linear nonlinearity. We construct the unperturbed limit cycle analytically, and are…

The limit cycle of the van der Pol oscillator, $\ddot{x}+ \epsilon (x^2-1) \dot{x} + x =0$, is studied in the plane $(x,\dot{x})$ by applying the homotopy analysis method. A recursive set of formulas that approximate the amplitude and form…

We study limit cycles of nonlinear oscillators described by the equation $\ddot x + \nu F(\dot x) + x =0$. Depending on the nonlinearity this equation may exhibit different number of limit cycles. We show that limit cycles correspond to…

Measurement-based control, utilizing an active feedback loop, is a standard tool in technology. Feedback control is also emerging as a useful and fundamental tool in quantum technology and in related fundamental studies, where it can be…

In the stochastic formulation of chemical kinetics, the stationary moments of the population count of species can be described via a set of linear equations. However, except for some specific cases such as systems with linear reaction…

Biochemical oscillations are ubiquitous in living organisms. In an autonomous system, not influenced by an external signal, they can only occur out of equilibrium. We show that they emerge through a generic nonequilibrium phase transition,…

In this paper, we describe a numerical continuation method that enables harmonic analysis of nonlinear periodic oscillators. This method is formulated as a boundary value problem that can be readily implemented by resorting to a standard…

Complex systems, such as biological networks, often exhibit intricate rhythmic behaviors that emerge from simple, small-amplitude dynamics in individual components. This study explores how significant oscillatory signals can arise from a…

We study theoretically the responsivity of optical modulators. For the case of linear response we find using perturbation theory an upper bound imposed upon the responsivity. For the case of two mode modulator we find a lower bound imposed…

Phase reduction is a well-established technique used to analyze the timing of oscillations in response to weak external inputs. In the preceding decades, a wide variety of results have been obtained for weakly perturbed oscillators that…

We obtain an almost sure bound for oscillation rates of empirical distribution functions for stationary causal processes. For short-range dependent processes, the oscillation rate is shown to be optimal in the sense that it is as sharp as…

Different types of synchronization states are found when non-linear chemical oscillators are embedded into an active medium that interconnects the oscillators but also contributes to the system dynamics. Using different theoretical tools,…

We discuss some frequency-domain criteria for the exponential stability of nonlinear feedback systems based on dissipativity theory. Applications are given to convergence rates for certain perturbations of the damped harmonic oscillator.

The aim of this paper is to survey and extend results concerning bounds of the Euclidean minima of abelian number fields. In particular, we give upper bounds for the Euclidean minima of abelian number fields of prime power conductor.

A new systematic approach to the construction of approximate solutions to a class of nonlinear singularly perturbed feedback control systems using the boundary layer functions especially with regard to the possible occurrence of the…

We provide a stochastic interpretation of non-commutative Dirichlet forms in the context of quantum filtering. For stochastic processes motivated by quantum optics experiments, we derive an optimal finite time deviation bound expressed in…

We derive a nonperturbative bound on the distance between evolutions of open quantum systems described by time-dependent generators. We show how this result can be employed to provide an explicit upper bound on the error of the…

Many crucial biological processes operate with surprisingly small numbers of molecules, and there is renewed interest in analyzing the impact of noise associated with these small numbers. Twenty--five years ago, Berg and Purcell showed that…

We propose a quantum feedback scheme for producing deterministically reproducible spin squeezing. The results of a continuous nondemolition atom number measurement are fed back to control the quantum state of the sample. For large samples…