Related papers: A periodic model for the dynamics of cell volume
Starting from a mesoscopic description of cell migration and intraspecific interactions we obtain by upscaling an effective reaction-difusion-taxis equation for the cell population density involving spatial nonlocalities in the source term…
We discuss several continuum cell-cell adhesion models based on the underlying microscopic assumptions. We propose an improvement on these models leading to sharp fronts and intermingling invasion fronts between different cell type…
We generalize the particle-conserving dynamics method of de las Heras et al. [J. Phys. Condens. Matter: 28, 24404 (2016).] to binary mixtures and apply this to hard rods in one dimension. Considering the case of one species consisting of…
We have developed a coarse-grained formulation for modeling the dynamic behavior of cells quantitatively, based on stochasticity and heterogeneity, rather than on biochemical reactions. We treat each reaction as a continuous-time stochastic…
We establish and prove a fixed point theorem from which some sufficient conditions on the existence of positive almost periodic solutions for a model of hematopoiesis with oscillatory circulation loss rate are deduced. Some particular…
Using continuation methods and bifurcation theory, we study the exact multiplicity of periodic solutions, and the global solution structure, for periodic problems of first order. The results are applied to a population model with fishing,…
In this work we proof that the one-body position operator for periodic systems that we have recently proposed [Phys. Rev. B 99, 205144] is unique modulo a phase factor and an additive constant. The proof uses several general physical…
Inspired by dense contractile tissues, where cells are subject to periodic deformation, we formulate and study a generic hydrodynamic theory of pulsating active liquids. Combining mechanical and phenomenological arguments, we postulate that…
In this work, a mathematical model of self-oscillatory dynamics of the metabolism in a cell is studied. The full phase-parametric characteristics of variations of the form of attractors depending on the dissipation of a kinetic membrane…
It is shown that the viscous-plastic Hibler sea ice model admits a unique, strong $T$-time periodic solution provided the given $T$-periodic forcing functions are small in suitable norms. This is in particular true for time periodic wind…
In this work the existence of a global attractor for the solution semiflow of the coupled two-cell Brusselator model equations is proved. A grouping estimation method and a new decomposition approach are introduced to deal with the…
Simple form scalar differential equation with delay and nonlinear negative periodic feedback is considered. The existence of several types of slowly oscillating periodic solutions is shown with the same and double periods of the feedback…
We consider an attraction-repulsion chemotaxis model coupled with the Navier-Stokes system. This model describes the interaction between a type of cells (e.g., bacteria), which proliferate following a logistic law, and two chemical signals…
We introduce a model for describing the dynamics of large numbers of interacting cells. The fundamental dynamical variables in the model are sub-cellular elements, which interact with each other through phenomenological intra- and…
This paper considers the dynamical behavior of solutions of constitutive systems for 1D compressible viscous and heat-conducting micropolar fluids. With proper constraints on initial data, we prove the existence of global attractors in…
As motivated by studies of cellular motility driven by spatiotemporal chemotactic gradients in microdevices, we develop a framework for constructing approximate analytical solutions for the location, speed and cellular densities for cell…
A simple non-autonomous scalar differential equation with delay, exponential decay, nonlinear negative feedback and a periodic multiplicative coefficient is considered. It is shown that stable slowly oscillating periodic solutions with the…
We study global-in-time behavior of the solution to a reaction-diffusion system with mass conservation, as proposed in the study of cell polarity, particularly, the second model of \cite{oi07}. First, we show global-in-time existence of…
We consider steady solutions to the incompressible Euler equations in a two-dimensional channel with rigid walls. The flow consists of two periodic layers of constant vorticity separated by an unknown interface. Using global bifurcation…
We consider a discrete time dynamic system described by a difference equation with periodic coefficients and with additive stochastic noise. We investigate the possibility of the periodicity for the solution. In particular, we found…