相关论文: Modeling oscillatory Microtubule--Polymerization
The response of lipid bilayers to osmotic stress is an important part of cellular function. Previously, in [Oglecka et al. 2014], we reported that cell-sized giant unilamellar vesicles (GUVs) exposed to hypotonic media, respond to the…
Molecular dynamics simulations are used to study fluidization of a vertically vibrated, three-dimensional shallow granular layer. As the container acceleration is increased above g, the granular temperature and root mean square particle…
An optomechanical oscillator undergoes a Hopf bifurcation that connects two dynamical regimes with different information-processing capabilities: thermal Brownian motion and coherent self-sustained oscillation. Below threshold, the…
Gene regulatory networks, i.e. DNA segments in a cell which interact with each other indirectly through their RNA and protein products, lie at the heart of many important intracellular signal transduction processes. In this paper we analyse…
We analyze the nonlinear dynamics near the incoherent state in a mean-field model of coupled oscillators. The population is described by a Fokker-Planck equation for the distribution of phases, and we apply center-manifold reduction to…
We show in a rigorous way that a stable internal single-layer stationary solution is destabilized by the Hopf bifurcation as the time constant exceeds a certain critical value. Moreover, the exact critical value and the exact period of…
We study strong-gravity effects on modulation of radiation emerging from accreting compact objects as a possible mechanism for flux modulation in QPOs. We construct a toy model of an oscillating torus in the slender approximation assuming…
We consider the model for the distribution of a long homopolymer in a potential field. The typical shape of the polymer depends on the temperature parameter. We show that at a critical value of the temperature the transition occurs from a…
The periodic modulation of an oscillator's frequency can lead to so-called parametric oscillations at half the driving frequency, which display bistability between two states whose phases differ by \pi. Such phase-locking bistability is at…
We study a modified Bullard dynamo and show that this system is equivalent to a nonlinear oscillator subject to a multiplicative noise. The stability analysis of this oscillator is performed. Two bifurcations are identified, first towards…
We study the linear instabilities and bifurcations in the Selkov model for glycolysis with diffusion. We show that this model has a zero wave-vector, finite frequency Hopf bifurcation to a growing oscillatory but spatially homogeneous state…
A periodic perturbation generates a complicated dynamics close to separatrices and saddle points. We construct an asymptotic solution which is close to the separatrix for the unperturbed Duffing's oscillator over a long time. This solution…
Oscillatory integrals arise in many situations where it is important to obtain decay estimates which are stable under certain perturbations of the phase. Examining the structural problems underpinning these estimates leads one to consider…
We describe a mechanism for pronounced biochemical oscillations, relevant to microscopic systems, such as the intracellular environment. This mechanism operates for reaction schemes which, when modeled using deterministic rate equations,…
We investigate an analytical treatment of bifurcations of families of resonant `thin' tubes in axisymmetric galactic potentials. We verify that the most relevant bifurcations are due to the (1:1) resonance producing the `inclined' orbits…
An approach is suggested for treating multiscale fluctuations in macromolecular systems. The emphasis is on the statistical properties of such fluctuations. The approach is illustrated by a macromolecular system with mesoscopic fluctuations…
We consider dynamical systems depending on one or more real parameters, and assuming that, for some ``critical'' value of the parameters, the eigenvalues of the linear part are resonant, we discuss the existence -- under suitable hypotheses…
In this study, a two-state mechanochemical model is presented to describe the dynamic instability of microtubules (MTs) in cells. The MTs switches between two states, assembly state and disassembly state. In assembly state, the growth of…
We study bifurcation for the constant scalar curvature equation along a one-parameter family of Riemannian metrics on the total space of a harmonic Riemannian submersion. We provide an existence theorem for bifurcation points and a…
The effect of decaying oscillatory perturbations on autonomous Hamiltonian systems in the plane with a stable equilibrium is investigated. It is assumed that perturbations preserve the equilibrium and satisfy a resonance condition. The…