Related papers: Diffusion and pattern formation in spatial games
A diffusive epidemic model with an infection-dependent recovery rate is formulated in this paper. Multiple constant steady states and spatially homogeneous periodic solutions are first proven by bifurcation analysis of the reaction…
Motivated by recent experiments and models of biological segmentation, we analyze the exicitation of pattern-forming instabilities of convectively unstable reaction-diffusion-advection (RDA) systems, occuring by means of constant or…
We investigate the influence of particle diffusion in the two-dimension contact process (CP) with a competitive dynamics in bipartite sublattices, proposed in [Phys. Rev. E 84, 011125 (2011)]. The particle creation depends on its first and…
Reaction-diffusion processes across layered media arise in several scientific domains such as pattern-forming E. coli on agar substrates, epidermal-mesenchymal coupling in development, and symmetry-breaking in cell polarisation. We develop…
Mathematical models of spatial population dynamics typically focus on the interplay between dispersal events and birth/death processes. However, for many animal communities, significant arrangement in space can occur on shorter timescales,…
Collective phenomena emerge from the interaction of natural or artificial units with a complex organization. The interplay between structural patterns and dynamics might induce functional clusters that, in general, are different from…
In social dilemmas self-interested learning agents face the choice between the societal benefit of cooperation and the immediate reward of defection. Significant evidence exists on the benefits of assortment mechanisms such as partner…
Coordination games with explicit spatial or relational structure are of interest to economists, ecologists, sociologists, and others studying emergent global properties in collective behavior. When assemblies of individuals seek to…
The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…
In this work, we investigate an intriguing and prevalent phenomenon of diffusion models which we term as "consistent model reproducibility": given the same starting noise input and a deterministic sampler, different diffusion models often…
The activity of biological cells is primarily based on chemical reactions and typically modeled as a reaction-diffusion system. Cells are, however, highly crowded with macromolecules, including a variety of molecular machines such as…
Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…
While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for efficiently training diffusion models for probabilistic spatiotemporal forecasting,…
It is known that the competitive exclusion principle holds for a large kind of models involving several species competing for a single resource in an homogeneous environment. Various works indicate that the coexistence is possible in an…
Motivated by the observation that anomalous diffusion is a realistic feature in the dynamics of biological populations, we investigate its implications in a paradigmatic model for the evolution of a single species density $u(x,t)$. The…
We investigate the phenomenon of diffusion in a countably infinite society of individuals interacting with their neighbors in a network. At a given time, each individual is either active or inactive. The diffusion is driven by two…
Most real life systems have a random component: the multitude of endogenous and exogenous factors influencing them result in stochastic fluctuations of the parameters determining their dynamics. These empirical systems are in many cases…
Diffusion processes are instrumental to describe the movement of a continuous quantity in a generic network of interacting agents. Here, we present a probabilistic framework for diffusion in networks and propose to classify agent…
Destructive agents, who opt out of the game and indiscriminately harm others, paradoxically foster cooperation, representing an intriguing variant of the voluntary participation strategy. Yet, their impact on cooperation remains…
Diffusion in the crowded environments of the biological membranes or materials interfaces often involves intermittent binding to surface proteins or defects. To account for this situation we study a 2-dimensional lattice gas in a field of…