Related papers: Distinguishing Feedback Mechanisms in Clock Models
A harmonic oscillator with time-dependent mass $m(t)$ and a time-dependent (squared) frequency $\omega^2(t)$ occurs in the modelling of several physical systems. It is generally believed that systems, with $m(t)>0$ and $\omega^2(t)>0$…
We present an implementation of a recently proposed procedure for defining time, based on the description of the evolving system and its clock as non-interacting, entangled systems, according to the Page and Wootters approach. We study how…
A theory of time-delayed coherent quantum feedback is developed. More specifically, we consider a quantum system coupled to a bosonic reservoir creating a unidirectional feedback loop. It is shown that the dynamics can be mapped onto a…
We review the construction and evolution of mathematical models of the Arabidopsis circadian clock, structuring the discussion into two distinct historical phases of modeling strategies: extension and reduction. The extension phase explores…
Dirac equation requires $E=mc^2$ energy of resting particle, leading to some $\exp(-iEt/\hbar)$ its evolution - periodic process of $\omega=mc^2/\hbar$ frequency, literally propelled by mass of particle, confirmed experimentally e.g. for…
Many biological systems can sense periodical variations in a stimulus input and produce well-timed, anticipatory responses after the input is removed. Such systems show memory effects for retaining timing information in the stimulus and…
In this work we address the question of how oscillations are arrested in the mouse somitogenesis clock when the determination front reaches presomitic cells. Based upon available experimental evidence we hypothesize that the mechanism…
We unify two different periodicity mechanisms: delayed self-regulation and planar predator-prey feedback. We consider scalar delay differential equations $\dot x(t) = rf(x(t), x(t - 1))$ where $f$ is monotone in the delayed component. Due…
Revivals of the coherent states of a deformed, adiabatically and cyclically varying oscillator Hamiltonian are examined. The revival time distribution is exactly that of Poincar\'{e} recurrences for a rotation map: only three distinct…
Multiple interlinked positive feedback loops shape the stimulus responses of various biochemical systems, such as the cell cycle or intracellular calcium release. Recent studies with simplified models have identified two advantages of…
We show that a ring of phase oscillators coupled with transmission delays can be used as a pattern recognition system. The introduced model encodes patterns as stable periodic orbits. We present a detailed analysis of the underlying…
Continuous clocks, i.e. the clocks that measure time in a continuous manner, are regarded as an essential component of sensing technology. Precision and recurrence time are two basic features of continuous clocks. In this paper, in the…
In order to study the "problem of time", Rovelli proposed a model of a two harmonic oscillator system where one of the oscillators can be thought of as a 'clock' for the other oscillator. In this paper we examine a model where the…
To understand the sophisticated control mechanisms of the human's endocrine system is a challenging task that is a crucial step towards precise medical treatment of many disfunctions and diseases. Although mathematical models describing the…
We study the implementation of a weak multiple delayed feedback for controlling coherence of chaotic oscillations. The specific system we treat is the Lorenz system with classical set of parameters. There are two reasons behind the interest…
Biomolecular oscillators can function robustly in the presence of environmental perturbations, which can either be static or dynamic. While the effect of different circuit parameters and mechanisms on the robustness to steady perturbations…
Adaptation to environmental change is a common property of biological systems. Cells initially respond to external changes in the environment, but after some time, they regain their original state. By considering an element consisting of…
Injection locking of optoelectronic oscillators (OEOs) with large delay gives rise to phase dynamics that lie beyond the scope of classical single mode locking theory, including the spontaneous formation of persistent $2\pi$ phase kinks. In…
We investigate the relation between the dynamics of a single oscillator with delayed self-feedback and a feed-forward ring of such oscillators, where each unit is coupled to its next neighbor in the same way as in the self-feedback case. We…
We study a two-variable dynamical system modeling pH oscillations in the urea-urease reaction within giant lipid vesicles -- a problem that intrinsically contains multiple, well-separated timescales. Building on an existing, deterministic…