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We study an individual-based model in which two spatially-distributed species, characterized by different diffusivities, compete for resources. We consider three different ecological settings. In the first, diffusing faster has a cost in…
Human mobility and activity patterns mediate contagion on many levels, including the spatial spread of infectious diseases, diffusion of rumors, and emergence of consensus. These patterns however are often dominated by specific locations…
We study the introduction of lexical innovations into a community of language users. Lexical innovations, i.e., new terms added to people's vocabulary, play an important role in the process of language evolution. Nowadays, information is…
Influence competition finds its significance in many applications, such as marketing, politics and public events like COVID-19. Existing work tends to believe that the stronger influence will always win and dominate nearly the whole…
In contrast to previous common wisdom that epidemic activity in heterogeneous networks is dominated by the hubs with the largest number of connections, recent research has pointed out the role that the innermost, dense core of the network…
Previous research on two-dimensional extensions of Hotelling's location game has argued that spatial competition leads to maximum differentiation in one dimensions and minimum differentiation in the other dimension. We expand on existing…
A great deal of significant progress has been seen in the study of information spreading on populations of networked individuals. A common point in many of past studies is that there is only one transition in the phase diagram of the final…
This paper studies a strategic model of marketing and product diffusion in social networks. We consider two firms offering substitutable products which can improve their market share by seeding the key individuals in the market. Consumers…
We investigate the dynamics of two agent based models of language competition. In the first model, each individual can be in one of two possible states, either using language $X$ or language $Y$, while the second model incorporates a third…
In this paper we present and analyse a simple two populations model with migrations among two different environments. The populations interact by competing for resources. Equilibria are investigated. A proof for the boundedness of the…
We introduce a model for the emergence of innovations, in which cognitive processes are described as random walks on the network of links among ideas or concepts, and an innovation corresponds to the first visit of a node. The transition…
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…
Innovation and evolution are two processes of paramount relevance for social and biological systems. In general, the former allows to introduce elements of novelty, while the latter is responsible for the motion of a system in its phase…
We consider the qualitative behavior of a mathematical model for transmission dynamics with two nonlinear stages of contagion. The proposed model is inspired by phenomena occurring in epidemiology (spread of infectious diseases) or social…
Resource competition is a fundamental interaction in natural communities.However little is known about competition in spatial environments where organisms are able to regulate resource distributions. Here, we analyze the competition of two…
We investigate a discrete-time two-strain symbiotic epidemic model on complex networks with both random and long-range interactions. Our analysis examines how the co-infection recovery rate ($\mu$), the long-range decay exponent ($\alpha$),…
The simultaneous emergence of several abrupt disease outbreaks or the extinction of some serotypes of multi-strain diseases are fingerprints of the interaction between pathogens spreading within the same population. Here, we propose a…
A key scientific challenge during the outbreak of novel infectious diseases is to predict how the course of the epidemic changes under different countermeasures that limit interaction in the population. Most epidemiological models do not…
We study diffusion on a multilayer network where the contact dynamics between the nodes is governed by a random process and where the waiting time distribution differs for edges from different layers. We study the impact on a random walk of…
Diffusion channels are critical to determining the adoption scale which leads to the ultimate impact of an innovation. The aim of this study is to develop an integrative understanding of the impact of two diffusion channels (i.e.,…