Related papers: Robust oscillations in multi-cyclic models of bioc…
Biological rhythms are generated by pacemaker organs, such as the heart pacemaker organ (the sinoatrial node) and the master clock of the circadian rhythms (the suprachiasmatic nucleus), which are composed of a network of autonomously…
Circadian rhythms are biological rhythms of approximately 24 h that persist even under constant conditions without environmental daily cues. The molecular circadian clock machinery generates the physiological rhythms, which can be…
Oscillation has an important role in bio-dynamical systems such as circadian rhythms and eukaryotic cell cycle. John Tyson et. al. in Nature Review Mol Cell Biol 2008 examined a limited number of network topologies consisting of three nodes…
Biochemical circadian rhythm oscillations play an important role in many signalling mechanisms. In this work, we explore some of the biophysical mechanisms responsible for sustaining robust oscillations by constructing a minimal but…
In networked systems, stochastic resonance occurs as a collective phenomenon where the entire stochastic network resonates with a weak applied periodic signal. Beyond the interplay among the network coupling, the amplitude of the external…
Oscillatory dynamics are ubiquitous in biological networks. Possible sources of oscillations are well understood in low-dimensional systems, but have not been fully explored in high-dimensional networks. Here we study large networks…
In probability theory, equalities are much less than inequalities. In this paper, we find a series of equalities which characterize the symmetry of the forming times of a family of similar cycles for discrete-time and continuous-time Markov…
In this work, we study the dynamical robustness in a system consisting of both active and inactive oscillators. We analytically show that the dynamical robustness of such system is determined by the cross link density between active and…
Coupled oscillator networks often display transitions between qualitatively different phase-locked solutions -- such as synchrony and rotating wave solutions -- following perturbation or parameter variation. In the limit of weak coupling,…
Biochemical clocks are essential for virtually all living systems. A biochemical clock that is isolated from an external periodic signal and subjected to fluctuations can oscillate coherently only for a finite number of oscillations.…
A variety of nonlinear models of biological systems generate complex chaotic behaviors that contrast with biological homeostasis, the observation that many biological systems prove remarkably robust in the face of changing external or…
Despite widespread and striking examples of physiological oscillations, their functional role is often unclear. Even glycolysis, the paradigm example of oscillatory biochemistry, has seen questions about its oscillatory function. Here, we…
We consider biochemical reaction chains and investigate how random external fluctuations, as characterized by variance and coefficient of variation, propagate down the chains. We perform such a study under the assumption that the number of…
Finite stochastic Markov models play a major role for modelling biochemical pathways. Such models are a coarse-grained description of the underlying microscopic dynamics and can be considered mesoscopic. The level of coarse-graining is to a…
It is generally recognized that a distinguishing feature of life is its peculiar capability to avoid equilibration. The origin of this capability and its evolution along the timeline of abiogenesis is not yet understood. We propose to study…
The circadian clocks keeping time of day in many living organisms rely on self-sustained biochemical oscillations which can be entrained by external cues, such as light, to the 24-hour cycle induced by Earth rotation. However, environmental…
A biochemical oscillator model, describing developmental stage of myxobacteria, is analyzed mathematically. Observations from numerical simulations show that in a certain range of parameters, the corresponding system of ordinary…
The synchronization stability of a complex network system of coupled phase oscillators is discussed. In case the network is affected by disturbances, a stochastic linearized system of the coupled phase oscillators may be used to determine…
In recent years it is increasingly being recognized that biochemical signals are not necessarily constant in time and that the temporal dynamics of a signal can be the information carrier. Moreover, it is now well established that…
Motivated by biochemical reaction networks, a generalization of the classical secant condition for the stability analysis of cyclic interconnected commensurate fractional-order systems is provided. The main result presents a sufficient…