Related papers: The symbiotic branching model: duality and interfa…
Previous work has shown that species interacting in an ecosystem and actors transacting in an economic context may have notable similarities in behavior. However, the specific mechanism that may underlie similarities in nature and human…
If two species exhibit different nonlinear responses to a single shared resource, and if each species modifies the resource dynamics such that this favors its competitor, they may stably coexist. This coexistence mechanism, known as…
We introduce spatially explicit stochastic processes to model multispecies host-symbiont interactions. The host environment is static, modeled by the infinite percolation cluster of site percolation. Symbionts evolve on the infinite cluster…
Cooperative interactions pervade in a broad range of many-body populations, such as ecological communities, social organizations, and economic webs. We investigate the dynamics of a population of two equivalent species A and B that are…
Both human-made and natural supply systems, such as power grids and leaf venation networks, are built to operate reliably under changing external conditions. Many of these spatial networks exhibit community structures. Here, we show that a…
Spatially dependent birth-death processes can be modelled by kinetic models such as the BBGKY hierarchy. Diffusion in infinite dimensional systems can be modelled with Brownian motion in Hilbert space. In this work Doi field theoretic…
Understanding the relationship between population and the built environment is essential for addresing socio-spatial inequalities. While researchers have long theorized these dynamics, empirical analyses remain limited. This study develops…
We present studies for an individual based model of three interacting populations whose individuals are mobile in a 2D-lattice. We focus on the pattern formation in the spatial distributions of the populations. Also relevant is the…
Consider a system $X = ((x_\xi(t)), \xi \in \Omega_N)_{t \geq 0}$ of interacting Fleming-Viot diffusions with mutation and selection which is a strong Markov process with continuous paths and state space $(\CP(\I))^{\Omega_N}$, where $\I$…
Motivated by a general principle governing regulation mechanisms in biological cells, we investigate a general interaction scheme between different populations of particles and specific particles, referred to as agents. Assuming that each…
Biological networks have two modes. The first mode is static: a network is a passage on which something flows. The second mode is dynamic: a network is a pattern constructed by gluing functions of entities constituting the network. In this…
The dynamics of diffusion in complex networks are widely studied to understand how entities, such as information, diseases, or behaviors, spread in an interconnected environment. Complex networks often present community structure, and tools…
A predator-prey model of dual populations with stochastic oscillators is presented. A linear cross-coupling between the two populations is introduced following the coupling between the motions of a Wilberforce pendulum in two dimensions:…
In this work we present a dynamical model that succesfully describes the organization of mutualistic ecological systems. The main characteristic of these systems is the nested structure of the bipartite adjacency matrix describing their…
We study the two-species symbiotic contact process (2SCP), recently proposed in [de Oliveira, Santos and Dickman, Phys. Rev. E {\bf 86}, 011121 (2012)] . In this model, each site of a lattice may be vacant or host single individuals of…
We consider a one-dimensional model consisting of an assembly of two-velocity particles moving freely between collisions. When two particles meet, they instantaneously annihilate each other and disappear from the system. Moreover each…
An individual-based model of stochastic branching is proposed and studied, in which point particles drift in $\bar{\mathds{R}}_{+}:=[0,+\infty)$ towards the origin (edge) with unit speed, where each of them splits into two particles that…
How diversity is maintained in natural ecosystems is a long-standing question in Theoretical Ecology. By studying a system that combines ecological dynamics, heterogeneous interactions and spatial structure, we uncover a new mechanism for…
We discuss two cases that can be connected to the dynamics of interacting populations: (I.) density waves for the case or negligible random fluctuations of the populations densities, and (II.) probability distributions connected to the…
A simple, but ``classical``, stochastic model for epidemic spread in a finite, but large, population is studied. The progress of the epidemic can be divided into three different phases that requires different tools to analyse. Initially the…