Related papers: Diffusion and pattern formation in spatial games
A local agglomeration of cooperators can support the survival or spreading of cooperation, even when cooperation is predicted to die out according to the replicator equation, which is often used in evolutionary game theory to study the…
Biological systems are majorly dependent on their property of bistability in order to exhibit nongenetic heterogeneity in terms of cellular morphology and physiology. Spatial patterns of phenotypically heterogeneous cells, arising due to…
Diffusion models have emerged as powerful generative models in the text-to-image domain. This paper studies their application as observation-to-action models for imitating human behaviour in sequential environments. Human behaviour is…
Fluctuating environments are situations where the spatio-temporal stochasticity plays a significant role in the evolutionary dynamics. The study of the evolution of cooperation in these environments typically assumes a homogeneous, well…
The spatial organization of individuals and their interactions in communities are important factors known to preserve diversity in many complex systems. Inspired by metapopulation models from ecology, we study opinion formation using a…
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…
Stochasticity is a defining feature of the pairwise forces governing interactions in biological systems-from molecular motors to cell-cell adhesion-yet its consequences on large-scale dynamics remain poorly understood. Here, we show that…
Differential diffusion is a source of instability in population dynamics systems when species diffuse with different rates. Predator-prey systems show this instability only under certain specific conditions, usually requiring Holling-type…
The costly provision of public goods serves as a model problem for the evolution of cooperative behavior, presenting a social dilemma between the collective benefits of shared resources and the individual incentive to free-ride in resource…
As humans perceive and actively engage with the world, we adjust our decisions in response to shifting group dynamics and are influenced by social interactions. This study aims to identify which aspects of interaction affect…
Spatial self-organization emerges in distributed systems exhibiting local interactions when nonlinearities and the appropriate propagation of signals are at work. These kinds of phenomena can be modeled with different frameworks, typically…
In the present work, we explore the influence of habitat complexity on the activities of prey and predator of a spatio-temporal system by incorporating self diffusion. First we modify the Rosenzweig-MacArthur predator-prey model by…
Cross-diffusion systems play a central role in mathematical modelling, in which density-dependent dispersal and multiscale mechanisms can lead to spatial segregation and diffusion-driven instabilities. In several relevant examples,…
Mechanisms of pattern formation---of which the Turing instability is an archetype---constitute an important class of dynamical processes occurring in biological, ecological and chemical systems. Recently, it has been shown that the Turing…
We investigate the effects of cooperativity between contagion processes that spread and persist in a host population. We propose and analyze a dynamical model in which individuals that are affected by one transmissible agent $A$ exhibit a…
The spatial arrangement of individuals is thought to overcome the dilemma of cooperation: When cooperators engage in clusters they might share the benefit of cooperation while being more protected against non-cooperating individuals, which…
Originating from the pioneering study of Alan Turing, the bifurcation analysis predicting spatial pattern formation from a spatially uniform state for diffusing morphogens or chemical species that interact through nonlinear reactions is a…
Understanding the pattern formation in communities has been at the center of attention in various fields. Here we introduce a novel model, called an "information-particle model," which is based on the reaction-diffusion model and the…
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…
Cooperation often depends on individuals avoiding exploitation and interacting preferentially with other cooperators. We explore how context-dependent migration influences the evolution of cooperation in spatially structured populations.…