Related papers: An introduction to linear stability analysis for d…
Reaction diffusion systems are often used to study pattern formation in biological systems. However, most methods for understanding their behavior are challenging and can rarely be applied to complex systems common in biological…
Signaling molecules play an important role for many cellular functions. We investigate here a general system of two membrane reaction-diffusion equations coupled to a diffusion equation inside the cell by a Robin-type boundary condition and…
The study of pattern emergence together with exploration of the exemplar Turing model is enjoying a renaissance both from theoretical and experimental perspective. Here, we implement a stability analysis of spatially dependent reaction…
Reaction-diffusion models have been used over decades to study biological systems. In this context, evolution equations for probability distribution functions and the associated stochastic differential equations have nowadays become…
Many systems in biology, physics and engineering can be described by systems of ordinary differential equation containing many parameters. When studying the dynamic behavior of these large, nonlinear systems, it is useful to identify and…
We study diffusion-driven pattern-formation in networks of networks, a class of multilayer systems, where different layers have the same topology, but different internal dynamics. Agents are assumed to disperse within a layer by undergoing…
The modelling of linear and nonlinear reaction-subdiffusion processes is more subtle than normal diffusion and causes different phenomena. The resulting equations feature a spatial Laplacian with a temporal memory term through a time…
Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a…
Steady state is an essential concept in reaction networks. Its stability reflects fundamental characteristics of several biological phenomena such as cellular signal transduction and gene expression. Because biochemical reactions occur at…
In this article, we carry out a study of long-term behavior of reaction-diffusion systems augmented with self- and cross-diffusion, using an augmented Gray-Scott system as a general example. The methodology remains generic, and is therefore…
A reaction--diffusion replicator equation is studied. A novel method to apply the principle of global regulation is used to write down the model with explicit spatial structure. Properties of stationary solutions together with their…
This paper provides the phase transition analysis of a reaction diffusion equations system modeling dynamic instability of microtubules. For this purpose we have generalized the macroscopic model studied by Mour\~ao et all [MSS]. This model…
This paper explores the classification of parameter spaces for reaction-diffusion systems of two chemical species on stationary domains. The dynamics of the system are explored both in the absence and presence of diffusion. The parameter…
In this work an activator-depleted reaction-diffusion system is investigated on polar coordinates with the aim of exploring the relationship and the corresponding influence of domain size on the types of possible diffusion-driven…
A variety of enhanced statistical and numerical methods are now routinely used to extract comprehensible and relevant thermodynamic information from the vast amount of complex, high-dimensional data obtained from intensive molecular…
Biochemical networks play a crucial role in biological systems, implementing a broad range of vital functions. They normally operate at low copy numbers and in spatial settings, but this is often ignored and well-stirred conditions are…
Reaction-diffusion models are widely used to study spatially-extended chemical reaction systems. In order to understand how the dynamics of a reaction-diffusion model are affected by changes in its input parameters, efficient methods for…
Feedback circuits in biochemical networks which underly cellular signaling pathways are important elements in creating complex behavior. A specific aspect thereof is how stability of equilibrium points depends on model parameters. For…
A molecule traveling in a realistic propagation environment can experience stochastic interactions with other molecules and the environment boundary. The statistical behavior of some isolated phenomena, such as dilute unbounded molecular…
In the past the study of reaction-diffusion systems has greatly contributed to our understanding of the behavior of many-body systems far from equilibrium. In this paper we aim at characterizing the properties of diffusion limited reactions…