Related papers: Swarm equilibria in domains with boundaries
We consider a class of physiologically structured population models, a first order nonlinear partial differential equation equipped with a nonlocal boundary condition, with a constant external inflow of individuals. We prove that the…
We study an evolutionary version of the spatial prisoner's dilemma game, where the agents are placed in a random graph. For lattices with fixed connectivity, $\alpha$, we show that for low values of $\alpha$ the final density of cooperating…
We construct equilibrium networks by introducing an energy function depending on the degree of each node as well as the product of neighboring degrees. With this topological energy function, networks constitute a canonical ensemble, which…
Current questions in ecology revolve around instabilities in the dynamics on spatial networks and particularly the effect of node heterogeneity. We extend the Master Stability Function formalism to inhomogeneous biregular networks having…
We establish the relation between local stability of equilibria and slopes of critical curves for a specific class of difference equations. We then use this result to give global behavior results for nonnegative solutions of the system of…
This paper studies a power transmission system with both conventional generators (CGs) and distributed energy assets (DEAs) providing frequency control. We consider an operating condition with demand aggregating two dynamic components: one…
A system made up of N interacting species is considered. Self-reaction terms are assumed of the logistic type. Pairwise interactions take place among species according to different modalities, thus yielding a complex asymmetric disordered…
We study the statistical behavior of two out of equilibrium systems. The first one is a quasi one-dimensional gas with two species of particles under the action of an external field which drives each species in opposite directions. The…
We study a system of coupled pendula with diffusive interactions, which could depend both on positions and on momenta. The coupling structure is defined by an undirected network, while the dynamic equations are derived from a Hamiltonian;…
A variational model for describing the morphology of two-phase continua by allowing for the interplay between coherent and incoherent interfaces is introduced. Coherent interfaces are characterized by the microscopical arrangement of atoms…
We undertake a fundamental study of network equilibria modeled as solutions of fixed point equations for monotone linear functions with saturation nonlinearities. The considered model extends one originally proposed to study systemic risk…
We consider load controlled quasistatic evolution. Well posedness results for the nonlocal continuum model related to peridynamics are established. We show local existence and uniqueness of quasistatic evolution for load paths originating…
Globally coupled ensembles of phase oscillators serve as useful tools for modeling synchronization and collective behavior in a variety of applications. As interest in the effects of simplicial interactions (i.e., non-additive, higher-order…
We consider any network environment in which the "best shot game" is played. This is the case where the possible actions are only two for every node (0 and 1), and the best response for a node is 1 if and only if all her neighbors play 0. A…
Reaction-diffusion equations coupled to ordinary differential equations (ODEs) may exhibit spatially low-regular stationary solutions. This work provides a comprehensive theory of asymptotic stability of bounded, discontinuous or…
In social networks, the balance theory has been studied by considering either the triple interactions between the links (structural balance) or the triple interaction of nodes and links (coevolutionary balance). In the structural balance…
We study the interaction between strategy, heterogeneity and growth in a two-agent model of capital accumulation. Preferences are represented by recursive utility functions with decreasing marginal impatience. The stationary equilibria of…
This paper is concerned with the Klein-Gordon-Maxwell system in a bounded spatial domain. We discuss the existence of standing waves $\psi=u(x)e^{-i\omega t}$ in equilibrium with a purely electrostatic field $\mathbf{E}=-\nabla\phi(x)$. We…
We present a general framework for modeling a wide selection of flocking scenarios under free boundary conditions. Several variants have been considered - including examples for the widely observed behavior of hierarchically interacting…
We study the collective behavior of nonequilibrium systems subject to an external field with a dynamics characterized by the existence of non-interacting states. Aiming at exploring the generality of the results, we consider two types of…