Related papers: Amplitude bounds for biochemical oscillators
We consider a one dimensional evolution problem modeling the dynamics of an acoustic field coupled with a set of mechanical oscillators. We analyze solutions of the system of ordinary and partial differential equations with time-dependent…
Many important complex networks, including critical infrastructure and emerging industrial automation systems, are becoming increasingly intricate webs of interacting feedback control loops. A fundamental concern is to quantify the control…
We prove lower bounds on the error incurred when approximating any oscillating function using piecewise polynomial spaces. The estimates are explicit in the polynomial degree and have optimal dependence on the meshwidth and frequency when…
The laws of quantum mechanics place fundamental limits on the accuracy of measurements and therefore on the estimation of unknown parameters of a quantum system. In this work, we prove lower bounds on the size of confidence regions reported…
A number of biological rhythms originate from networks comprised of multiple cellular oscillators. But analytical results are still lacking on the collective oscillation period of inter-coupled gene regulatory oscillators, which, as has…
A new method is presented for the analysis of limit cycle oscillations in mixed-feedback systems. The calculation of the limit cycle is reformulated as the zero finding of a mixed-monotone relation, that is, of the difference of two…
We present a design framework to induce stable oscillations through mixed feedback control. We provide conditions on the feedback gain and on the balance between positive and negative feedback contributions to guarantee robust oscillations.…
Feedback is a most important concept in control systems, its main purpose is to deal with internal and/or external uncertainties in dynamical systems, by using the on-line observed information. Thus, a fundamental problem in control theory…
In recent decades, several mathematical models describing the pacemaker activity of the rabbit sinoatrial node have been developed. We demonstrate that it is not possible to establish the existence, uniqueness, and stability of a limit…
We demonstrate an analytical method for calculating the phase sensitivity of a class of oscillators whose phase does not affect the time evolution of the other dynamic variables. We show that such oscillators possess the possibility for…
Diverse physical systems are characterized by their response to small perturbations. Near thermodynamic equilibrium, the fluctuation-dissipation theorem provides a powerful theoretical and experimental tool to determine the nature of…
Bioreactors are widely used in many industries to generate a range of products using various host cells e.g., yeast, insect, and mammalian cells. Depending on the process, product, and host cell, some bioreactors exhibit sustained periodic…
The mixed initial-boundary value problem for infinite one-dimensional chain of harmonic oscillators on the half-line is considered. We study the large time behavior of solutions and derive the dispersive bounds.
Some limit theorems are proven for the linear oscillator with random coefficients. The asymptotic behaviour of the moments is studied in detail. The technique presented in this paper can be applied to general linear systems with noise and…
We show that Nechiporuk's method for proving lower bounds for Boolean formulas can be extended to the quantum case. This leads to an $\Omega(n^2 / \log^2 n)$ lower bound for quantum formulas computing an explicit function. The only known…
A description in terms of phase and amplitude variables is given, for nonlinear oscillators subject to white Gaussian noise described by It\^o stochastic differential equations. The stochastic differential equations derived for the…
In an oscillatory medium, a region which oscillates faster than its surroundings can act as a source of outgoing waves. Such pacemaker-generated waves can synchronize the whole medium and are present in many chemical and biological systems,…
Autonomous oscillators, such as clocks and lasers, produce periodic signals \emph{without} any external frequency reference. In order to sustain stable periodic motions, there needs to be external energy supply as well as nonlinearity built…
Biomolecular feedback systems are now a central application area of interest within control theory. While classical control techniques provide invaluable insight into the function and design of both natural and synthetic biomolecular…
In this paper, we present a novel estimation and control strategy to balance a formation of discrete-time oscillators on a circle. We consider the case in which each oscillator only gathers noisy proximity measurements, whose range is lower…