Related papers: Master stability functions reveal diffusion-driven…
Dynamical reaction-diffusion processes and meta-population models are standard modeling approaches for a wide variety of phenomena in which local quantities - such as density, potential and particles - diffuse and interact according to the…
Decisions to disperse from a habitat stand out among organismal behaviors as pivotal drivers of ecosystem dynamics across scales. Encounters with other species are an important component of adaptive decision-making in dispersal, resulting…
Networks are a widely used and efficient paradigm to model real-world systems where basic units interact pairwise. Many body interactions are often at play, and cannot be modelled by resorting to binary exchanges. In this work, we consider…
We develop a novel approach to study the global behaviour of large foodwebs for ecosystems where several species share multiple resources. The model extends and generalize some previous works and takes into account self-limitation. Under…
Bacteria can form a great variety of spatially heterogeneous cell density patterns, ranging from simple concentric rings to dynamical spiral waves appearing in growing colonies. These pattern formation phenomena are important as they…
The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are…
Climate change is reshaping species interactions and movement across fragmented landscapes. Despite this, most mathematical models assume random diffusion, overlooking the influence of directed movement. Here, we develop a graph based…
Diffusion dynamics in multiplex networks can model a diverse number of real-world processes. In some specific configurations of these systems, the super-diffusion phenomenon arises, in which the diffusion is faster in the multiplex network…
Dynamic multilayer networks frequently represent the structure of multiple co-evolving relations; however, statistical models are not well-developed for this prevalent network type. Here, we propose a new latent space model for dynamic…
We explore a simplified class of models we call swarms, which are inspired by the collective behavior of social insects. We perform a mean-field stability analysis and perform numerical simulations of the model. Several interesting types of…
In the study of dynamical systems on networks/graphs, a key theme is how the network topology influences stability for steady states or synchronized states. Ideally, one would like to derive conditions for stability or instability that…
Real-world datasets are inherently heterogeneous, yet how per-class structural differences and sampling imbalance shape the training dynamics of diffusion models-and potentially exacerbate disparities-remains poorly understood. While models…
In this paper, we address the problem of dynamic network embedding, that is, representing the nodes of a dynamic network as evolving vectors within a low-dimensional space. While the field of static network embedding is wide and…
Humans naturally obtain intuition about the interactions between and the stability of rigid objects by observing and interacting with the world. It is this intuition that governs the way in which we regularly configure objects in our…
The stability of ecosystems as well as the relation between topology and dynamics on multilayer networks are important questions that are usually discussed in separate communities. Here, we combine these two topics by investigating the…
Diffusion describes the motion of microscopic entities from regions of high concentration to regions of low concentration. In multiplex networks, flows can occur both within and across layers, and super-diffusion, a regime where the time…
We investigate global stability and dynamics of large ecological networks by classical methods of the dynamical system theory, including Hamiltonian methods, and averaging. Our analysis exploits the network topological structure, namely,…
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…
Biological networks of interacting agents exhibit similar topological properties for a wide range of scales, from cellular to ecological levels, suggesting the existence of a common evolutionary origin. A general evolutionary mechanism…
We perform the linear stability analysis for a new model for poromechanical processes with inertia (formulated in mixed form using the solid deformation, fluid pressure, and total pressure) interacting with diffusing and reacting solutes…