Related papers: Swarm equilibria in domains with boundaries
Strong local minimizers with surfaces of gradient discontinuity appear in variational problems when the energy density function is not rank-one convex. In this paper we show that stability of such surfaces is related to stability outside…
Long-range interacting Hamiltonian systems are believed to relax generically towards non-equilibrium states called "quasi-stationary" because they evolve towards thermodynamic equilibrium very slowly, on a time-scale diverging with particle…
In this paper, we use a variety of mathematical techniques to explore existence, local stability, and global stability of equilibria in abstract models of mitochondrial metabolism. The class of models constructed is defined by the…
In this paper we study social exclusion in social (information) networks using a game-theoretic approach, and study the stability of a certain class community structures that are a Nash equilibrium. The main result of our analysis shows…
The real Ginzburg-Landau equation possesses a family of spatially periodic equilibria. If the wave number of an equilibrium is strictly below the so called Eckhaus boundary the equilibrium is known to be spectrally and diffusively stable,…
How do networks of relationships evolve over time? We analyse a dataset tracking the social interactions of 900 individuals over four years. Despite continuous shifts in individual relationships, the macroscopic structural properties of the…
The stability of stationary solutions of first-order systems of PDE's are considered. They may include some singular geometric terms, leading to discontinuous flux and non-conservative products. Based on several examples in Fluid Mechanics,…
We consider swarms formed by populations of self-propelled particles with attractive long-range interactions. These swarms represent multistable dynamical systems and can be found either in coherent traveling states or in an incoherent…
We introduce and study a nonlinear discrete dynamical system describing the evolution of a resource distribution among interacting agents. The model generalizes several classical mean-field and opinion-dynamics frameworks and is defined on…
There are rich emergent phase behaviors in non-equilibrium active systems. Flocking and clustering are two representative dynamic phases. The relationship between these two phases is still unclear. In the paper, we numerically investigate…
Social networks of engagement sometimes dramatically collapse. A widely adopted paradigm to understand this catastrophe dynamics is the threshold model but previous work only considered the irreversible K-core pruning process and the…
We analyze the non-equilibrium order-disorder transition of Axelrod's model of social interaction in several complex networks. In a small world network, we find a transition between an ordered homogeneous state and a disordered state. The…
We consider the dynamics of semiflows of patterns on unbounded domains that are equivariant under a noncompact group action. We exploit the unbounded nature of the domain in a setting where there is a strong `global' norm and a weak `local'…
A central feature of complex systems is the relevance and entanglement of different levels of description. For instance, the dynamics of ecosystems can be alternatively described in terms of large ecological processes and classes of…
Sensory mechanisms in biology, from cells to humans, have the property of adaptivity, whereby the response produced by the sensor is adapted to the overall amplitude of the signal; reducing the sensitivity in the presence of strong…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
We consider reaction-diffusion systems and other related dissipative systems on unbounded domains which would have a Liapunov function (and gradient structure) when posed on a finite domain. In this situation, the system may reach local…
A possible approach to description of the non equilibrium system has been proposed. Based on the Fokker-Plank equation in term of energy for non equilibrium distribution function of macroscopical system was obtained the stationary solution…
Characterizing the in uence of network properties on the global emerging behavior of interacting elements constitutes a central question in many areas, from physical to social sciences. In this article we study a primary model of disordered…
Order can spontaneously emerge from seemingly noisy interactions between biological agents, like a flock of birds changing their direction of flight in unison, without a leader or an external cue. We are interested in the generic conditions…