Related papers: A Calvin bestiary
In this work, we revisit the classical Holling type II three species food chain model with a different viewpoint. Two critical parameters $\lambda_1$ and $\lambda_2$ dependent on other six parameters are defined. We show that local…
We investigate the stability properties of two different classes of metabolic cycles using a combination of analytical and computational methods. Using principles from structural kinetic modeling (SKM), we show that the stability of…
To develop and investigate detailed mathematical models of cellular metabolic processes is one of the primary challenges in systems biology. However, despite considerable advance in the topological analysis of metabolic networks, explicit…
The multisite phosphorylation-dephosphorylation cycle is a motif repeatedly used in cell signaling. This motif itself can generate a variety of dynamic behaviors like bistability and ultrasensitivity without direct positive feedbacks. In…
Colloidal model systems allow studying crystallization kinetics under fairly ideal conditions with rather well characterized pair interactions and minimized external influences. In complementary approaches therefore experiment, analytic…
Mathematical models of glucose, insulin, and pancreatic $\beta$-cell mass dynamics are essential for understanding the physiological basis of type 2 diabetes. This paper investigates the Topp model's discrete-time dynamics to represent…
The three species asymmetric ABC model was initially defined on a ring by Evans, Kafri, Koduvely, and Mukamel, and the weakly asymmetric version was later studied by Clincy, Derrida, and Evans. Here the latter model is studied on a…
A geometrical model which captures the main ingredients governing atom-diatom collinear chemical reactions is proposed. This model is neither near-integrable nor hyperbolic, yet it is amenable to analysis using a combination of the recently…
In this work, we suggest a system of differential equations that quantitatively models the formulation and evolution of a trend cycle through the consideration of underlying dynamics between the trend participants. Our model captures the…
A simple model of particle creation and annihilation in an isolated assembly of particles with conserved energy and fixed volume, the Cell Model, is formulated. With increasing time, particle number distribution, obtained by averaging over…
This is a continuation of the previous work (Takata & Noguchi, J. Stat. Phys., 2018) that introduces the presumably simplest model of kinetic theory for phase transition. Here, main concern is to clarify the stability of uniform equilibrium…
In this paper, we explore pattern formation in a four-species variational Gary-Scott model, which includes all reverse reactions and introduces a virtual species to describe the birth-death process in the classical Gray-Scott model. This…
We introduce a two-dimensional Keller-Segel type free boundary model for motility of eukaryotic cells on substrates. The key ingredients of this model are the Darcy law for overdamped motion of the cytoskeleton (active) gel and Hele-Shaw…
The classical one-phase Stefan problem (without surface tension) allows for a continuum of steady state solutions, given by an arbitrary (but sufficiently smooth) domain together with zero temperature. We prove global-in-time stability of…
Parametrized polynomial ordinary differential equation systems are broadly used for modeling, specially in the study of biochemical reaction networks under the assumption of mass-action kinetics. Understanding the qualitative behavior of…
Concepts like `typicality' and the `eigenstate thermalization hypothesis' aim at explaining the apparent equilibration of quantum systems, possibly after a very long time. However, these concepts are not concerned with the specific way in…
We consider the Schr\"odinger--Poisson--Newton equations for crystals with a cubic lattice and one ion per cell. We linearize this dynamics at the ground state and introduce a novel class of the ion charge densities which provide the…
A system made up of N interacting species is considered. Self-reaction terms are assumed of the logistic type. Pairwise interactions take place among species according to different modalities, thus yielding a complex asymmetric disordered…
We study the scenarios of the dynamics of ternary statistical experiments, modeled employing difference equations. The important features are a balance condition and the existence of a steady-state (equilibrium). We give a classification of…
A novel model of biological organisms is advanced, treating an organism as a self-consistent system subject to a pathogen flux. The principal novelty of the model is that it describes not some parts, but a biological organism as a whole.…