Related papers: Swarm equilibria in domains with boundaries
We study an intrinsic model for collective behaviour on the hyperbolic space $\bbh^\dm$. We investigate the equilibria of the aggregation equation (or equivalently, the critical points of the associated interaction energy) for interaction…
We investigate a general class of models for swarming/self-collective behaviour in domains with boundaries. The model is expressed as a stochastic system of interacting particles subject to both reflecting boundary condition and common…
We concentrate on kinetic models for swarming with individuals interacting through self-propelling and friction forces, alignment and noise. We assume that the velocity of each individual relaxes to the mean velocity. In our present case,…
For a symmetric Hamiltonian system, lower bounds for the number of relative equilibria surrounding stable and formally unstable relative equilibria on nearby energy levels are given.
This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution. Either the solution behaves in an oscillatory, quasiperiodic manner or the nonlinear effects cause…
We study equilibrium states for an open class of non-uniformly expanding local homeomorphisms defined by a mild condition such that for some iterate each point admits at least one contracting inverse branch. We prove the existence and…
A class of models with applications to swarm behavior as well as many other types of spatially extended complex biological and physical systems is studied. Internal fluctuations can play an active role in the organization of the phase…
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…
This paper studies the boundary behaviour at mechanical equilibrium at the ends of a finite interval of a class of systems of interacting particles with monotone decreasing repulsive force. Our setting covers pile-ups of dislocations,…
We model a close-knit community of friends and enemies as a fully connected network with positive and negative signs on its edges. Theories from social psychology suggest that certain sign patterns are more stable than others. This notion…
We consider the out-of-equilibrium dynamics generated by joining two domains with arbitrary opposite magnetisations. We study the stationary state which emerges by the unitary evolution via the spin $1/2$ XXZ Hamiltonian, in the gapless…
Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…
We study the influence of boundary conditions on stationary, periodic patterns in one-dimensional systems. We show how a conceptual understanding of the structure of equilibria in large domains can be based on the characterization of…
In complex ecological communities, species may self-organize into clusters or clumps where highly similar species can coexist. The emergence of such species clusters can be captured by the interplay between neutral and niche theories. Based…
In this paper the motion of two-phase, incompressible, viscous fluids with surface tension is investigated. Three cases are considered: (1) the case of heat-conducting fluids, (2) the case of isothermal fluids, and (3) the case of Stokes…
We propose a new mean-field game model with two states to study synchronization phenomena, and we provide a comprehensive characterization of stationary and dynamic equilibria along with their stability properties. The game undergoes a…
In this paper, we prove a stability result for an elastodynamic system with acoustic boundary conditions and localized internal damping, defined in a bounded domain $\Omega$ of $\mathbb{R}^3$. Here, the internal damping is only assumed to…
In this paper, we use dynamical systems to analyze stability of desynchronization algorithms at equilibrium. We start by illustrating the equilibrium of a dynamic systems and formalizing force components and time phases. Then, we use Linear…
We study the equilibrium states of energy functions involving a large set of real variables, defined on the links of sparsely connected networks, and interacting at the network nodes, using the cavity and replica methods. When applied to…
We consider systems that are well modelled as a networks that evolve in time, which we call {\it Moving Neighborhood Networks}. These models are relevant in studying cooperative behavior of swarms and other phenomena where emergent…