Related papers: Detecting minimum energy states and multi-stabilit…
Vegetation patterns are a ubiquitous feature of water-deprived ecosystems. Despite the competition for the same limiting resource, coexistence of several plant species is commonly observed. We propose a two-species reaction-diffusion model…
Understanding the assembly of ecosystems to estimate the number of species at different spatial scales is a challenging problem. Until now, maximum entropy approaches have lacked the important feature of considering space in an explicit…
Coexistence of different geometric shapes at low energies presents a universal structure phenomenon that occurs over the entire chart of nuclides. Studies of the shape coexistence are important for understanding the microscopic origin of…
Microbial ecosystems are remarkably diverse, stable, and often consist of a balanced mixture of core and peripheral species. Here we propose a conceptual model exhibiting all these emergent properties in quantitative agreement with real…
We study a reaction-diffusion equation with an integral term describing nonlocal consumption of resources. We show that a homogeneous equilibrium can lose its stability resulting in appearance of stationary spatial structures. It is a new…
Dense suspensions of self-propelled rod-like particles exhibit a fascinating variety of non-equilibrium phenomena. By means of computer simulations of a minimal model for rigid self-propelled colloidal rods with variable shape we explore…
Natural ecosystems are characterized by striking diversity of form and functions and yet exhibit deep symmetries emerging across scales of space, time and organizational complexity. Species-area relationships and species-abundance…
In many biological systems, motile agents exhibit random motion with short-term directional persistence, together with crowding effects arising from spatial exclusion. We formulate and study a class of lattice-based models for multiple…
Over the past century, nonlinear difference and differential equations have been used to understand conditions for species coexistence. However, these models fail to account for random fluctuations due to demographic and environmental…
The paper focuses on positive solutions to a coupled system of parabolic equations with nonlocal initial conditions. Such equations arise as steady-state equations in an age-structured predator-prey model with diffusion. By using global…
We study the spatial pattern formation and emerging long range correlations in a model of three species coevolving in space and time according to stochastic contact rules. Analytical results for the pair correlation functions, based on a…
The problem of finding the minimum-energy configuration of particles on a lattice, subject to a generic short-ranged repulsive interaction, is studied analytically. The study is relevant to charge ordered states of interacting fermions, as…
Aggregations are emergent features common to many biological systems. Mathematical models to understand their emergence are consequently widespread, with the aggregation-diffusion equation being a prime example. Here we study the…
We consider an aggregation model for two interacting species. The coupling between the species is via their velocities, that incorporate self- and cross-interactions. Our main interest is categorizing the possible steady states of the…
We revisit a classical continuum model for the diffusion of multiple species with size-exclusion constraint, which leads to a degenerate nonlinear cross-diffusion system. The purpose of this article is twofold: first, it aims at a…
Pattern formation is a widely observed phenomenon in diverse fields including materials physics, developmental biology and ecology, among many others. The physics underlying the patterns is specific to the mechanisms, and is encoded by…
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…
In any ecosystem, the conditions of the environment and the characteristics of the species that inhabit it are entangled, co-evolving in space and time. We introduce a model that couples active agents with a dynamic environment, interpreted…
Many biological processes are supported by special molecules, called motor proteins or molecular motors, that transport cellular cargoes along linear protein filaments and can reversibly associate to their tracks. Stimulated by these…
Highly-diverse ecosystems exhibit a broad distribution of population sizes and species turnover, where species at high and low abundances are exchanged over time. We show that these two features generically emerge in the fluctuating phase…