Related papers: Reaction-Diffusion Systems as Complex Networks
This paper develops the concept of decomposition for chemical reaction networks, based on which a network decomposition technique is proposed to capture the stability of large-scale networks characterized by a high number of species, high…
We propose a technique to detect and generate patterns in a network of locally interacting dynamical systems. Central to our approach is a novel spatial superposition logic, whose semantics is defined over the quad-tree of a partitioned…
Over the last decade, an enormous interest and activity in complex networks have been witnessed within the physics community. On the other hand, diffusion and its theory, have equipped the toolbox of the physicist for decades. In this…
Cataloging the complex behaviors of dynamical systems can be challenging, even when they are well-described by a simple mechanistic model. If such a system is of limited analytical tractability, brute force simulation is often the only…
Predicting counterfactual distributions in complex dynamical systems is essential for scientific modeling and decision-making in domains such as public health and medicine. However, existing methods often rely on point estimates or purely…
Reaction networks are a general formalism for describing collections of classical entities interacting in a random way. While reaction networks are mainly studied by chemists, they are equivalent to Petri nets, which are used for similar…
Robustness of spatial pattern against perturbations is an indispensable property of developmental processes for organisms, which need to adapt to changing environments. Although specific mechanisms for this robustness have been extensively…
Accurately determining and classifying the structure of complex networks is the focus of much current research. One class of network of particular interest are metabolic pathways, which have previously been studied from a graph theoretical…
Nakao and Mikhailov proposed using continuous models (mean-field models) to study reaction-diffusion systems on networks and the corresponding Turing patterns. This work aims to show that p-adic analysis is the natural tool to carry out…
This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from…
This paper investigates the long-term dynamics of a reaction-diffusion predator-prey system subject to random environmental fluctuations modeled by Markovian switching. The model is formulated as a hybrid system of partial differential…
The large-scale organization of complex networks, both natural and artificial, has shown the existence of highly heterogeneous patterns of organization. Such patterns typically involve scale-free degree distributions and small world,…
The spread of new ideas, behaviors or technologies has been extensively studied using epidemic models. Here we consider a model of diffusion where the individuals' behavior is the result of a strategic choice. We study a simple coordination…
We show that solutions of the chemical reaction-diffusion system associated to $A+B\rightleftharpoons C$ in one spatial dimension can be approximated in $L^2$ on any finite time interval by solutions of a space discretized ODE system which…
This is a pedagogical account on reaction-diffusion systems and their relationship with integrable quantum spin chains. Reaction-diffusion systems are paradigmatic examples of non-equilibrium systems. Their long-time behaviour is strongly…
Networks effectively capture interactions among components of complex systems, and have thus become a mainstay in many scientific disciplines. Growing evidence, especially from biology, suggest that networks undergo changes over time, and…
We analyze a class of cell-bulk coupled PDE-ODE models, motivated by quorum and diffusion sensing phenomena in microbial systems, that characterize communication between localized spatially segregated dynamically active signaling…
The reaction of volatile matter plays an important role in the process of bringing matter from the surface of the planet to the atmosphere. Therefore, by simulating the mixing and chemical reaction process of volatile matter in the…
Understanding anomalous transport and reaction kinetics due to microscopic physical and chemical disorder is a long-standing goal in many fields including geophysics, biology, and engineering. We consider reaction-diffusion characterized by…
In recent years the research community has accumulated overwhelming evidence for the emergence of complex and heterogeneous connectivity patterns in a wide range of biological and sociotechnical systems. The complex properties of real-world…