Related papers: The lingering phenomenon and pattern formation in …
We propose a model to characterize how a diffusing population adapts under a time periodic selection, while its environment undergoes shifts and size changes, leading to significant differences with classical results on fixed domains. After…
Cities are typical dynamic complex systems that connect people and facilitate interactions. Revealing universal collective patterns behind spatio-temporal interactions between residents is crucial for various urban studies, of which we are…
We explore how different types and uses of memory can aid spatial navigation in changing uncertain environments. In the simple foraging task we study, every day, our agent has to find its way from its home, through barriers, to food.…
The hippocampus supports spatial navigation by encoding cognitive maps through collective place cell activity. We model the place cell population as non-negative spatial embeddings derived from the spectral decomposition of multi-step…
We consider the problem of diffusion with stochastic resetting in a population of random walks where the diffusion coefficient is not constant, but behaves as a power-law of the average resetting rate of the population. Resetting occurs…
Living in groups brings benefits to many animals, such as a protection against predators and an improved capacity for sensing and making decisions while searching for resources in uncertain environments. A body of studies has shown how…
The growth of a population divided among spatial sites, with migration between the sites, is sometimes modelled by a product of random matrices, with each diagonal elements representing the growth rate in a given time period, and…
Population boundary is a classic indicator of climatic response in ecology. In addition to known challenges, the spatial and dynamical characteristics of the boundary are not only affected by the spatial gradient in the environmental…
We are interested in populations in which the fitness of different genetic types fluctuates in time and space, driven by temporal and spatial fluctuations in the environment. For simplicity, our population is assumed to be composed of just…
Population structure induced by both spatial embedding and more general networks of interaction, such as model social networks, have been shown to have a fundamental effect on the dynamics and outcome of evolutionary games. These effects…
We consider a population dynamics model coupling cell growth to a diffusion in the space of metabolic phenotypes as it can be obtained from realistic constraints-based modelling. In the asymptotic regime of slow diffusion, that coincides…
The spatial segregation of species is fundamental to ecosystem formation and stability. Behavioural strategies may determine where species are located and how their interactions change the local environment arrangement. In response to…
This paper addresses the question of how population diffusion affects the formation of the spatial patterns in the spatial epidemic model by Turing mechanisms. In particular, we present theoretical analysis to results of the numerical…
We demonstrate that demographic noise can induce persistent spatial pattern formation and temporal oscillations in the Levin-Segel predator-prey model for plankton-herbivore population dynamics. Although the model exhibits a Turing…
This paper studies spatial patterns formed by proximate population migration driven by real wage gradients and other idiosyncratic factors. The model consists of a tractable core-periphery model incorporating a quasi-linear log utility…
Populations interact non-linearly and are influenced by environmental fluctuations. In order to have realistic mathematical models, one needs to take into account that the environmental fluctuations are inherently stochastic. Often,…
Attractor networks are an influential theory for memory storage in brain systems. This theory has recently been challenged by the observation of strong temporal variability in neuronal recordings during memory tasks. In this work, we study…
When biological populations expand into new territory, the evolutionary outcomes can be strongly influenced by genetic drift, the random fluctuations in allele frequencies. Meanwhile, spatial variability in the environment can also…
Migration is a key mechanism for expansion of communities. In spatially heterogeneous environments, rapidly gaining knowledge about the local environment is key to the evolutionary success of a migrating population. For historical human…
Consider a stochastic process that behaves as a $d$-dimensional simple and symmetric random walk, except that, with a certain fixed probability, at each step, it chooses instead to jump to a given site with probability proportional to the…