Related papers: Robustness of clocks to input noise
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…
In a noisy environment, oscillations loose their coherence which can be characterized by a quality factor. We determine this quality factor for oscillations arising from a driven Fokker-Planck dynamics along a periodic one-dimensional…
The mammalian circadian system comprises a network of cell-autonomous oscillators, spanning from the central clock in the brain to peripheral clocks in other organs. These clocks are tightly coordinated to orchestrate rhythmic physiological…
Theoretical models that describe oscillations in biological systems are often either a limit cycle oscillator, where the deterministic nonlinear dynamics gives sustained periodic oscillations, or a noise-induced oscillator, where a fixed…
The circadian clock is the molecular mechanism responsible for the adaptation to daily rhythms in living organisms. Oscillations and fluctuations in environmental conditions regulate the circadian clock through signaling pathways. We study…
The cyanobacterium Synechococcus elongatus uses both a protein phosphorylation cycle and a transcription-translation cycle to generate circadian rhythms that are highly robust against biochemical noise. We use stochastic simulations to…
The ability of a circadian system to entrain to the 24-hour light-dark cycle is one of its most important properties. A new tool, called the entrainment map, was recently introduced to study this process for a single oscillator. Here we…
In classical physics, clocks are open dissipative systems driven from thermal equilibrium and necessarily subject to thermal noise. We describe a quantum clock driven by entropy reduction through measurement. The mechanism consists of a…
In this paper, we present a novel framework for quantifying a lower bound on resilience in continuous-time (non)linear systems subject to external disturbances while ensuring satisfaction of signal temporal logic specifications. Unlike…
Circadian clocks exhibit the robustness of period and plasticity of phase against environmental changes such as temperature and nutrient conditions. Thus far, however, it is unclear how both are simultaneously achieved. By investigating…
Brownian clocks are biomolecular networks that can count time. A paradigmatic example are proteins that go through a cycle thus regulating some oscillatory behaviour in a living system. Typically, such a cycle requires free energy often…
Limit-cycle oscillators are the basic building blocks for synchronization; yet, the notion of a quantum limit cycle has remained unclear. Here, we study quantum limit cycles and synchronization in the presence of continuous heterodyne…
Circadian clocks play a pivotal role in orchestrating numerous physiological and developmental events. Waveform shapes of the oscillations of protein abundances can be informative about the underlying biochemical processes of circadian…
Many physical and biological systems exhibit intrinsic cyclic dynamics that are altered by random external perturbations. We examine continuous-time autonomous dynamical systems exhibiting a stable limit cycle, perturbed by additive…
Inspired by the observation of a distributed time delay in the nonlinear response of an optical resonator, we investigate the effects of a similar delay on a noise-driven mechanical oscillator. For a delay time that is commensurate with the…
Weakly coupled oscillators adjust their dynamics to work in unison: they synchronize. This ubiquitous phenomenon is observed for oscillating pendulum, electronic devices, as well as clapping crowds or flashing fireflies. In effect,…
Circadian rhythms are archetypical examples of nonlinear oscillations. While these oscillations are usually attributed to circuits of biochemical interactions among clock genes and proteins, recent experimental studies reveal that they are…
The phase description is a powerful tool for analyzing noisy limit cycle oscillators. The method, however, has found only limited applications so far, because the present theory is applicable only to the Gaussian noise while noise in the…
There are many different types of time keeping devices. We use the phrase ticking clock to describe those which -- simply put -- "tick" at approximately regular intervals. Various important results have been derived for ticking clocks, and…
We study the effect of additive Brownian noise on an ODE system that has a stable hyperbolic limit cycle, for initial data that are attracted to the limit cycle. The analysis is performed in the limit of small noise - that is, we modulate…