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We analyze under which conditions equilibration between two competing effects, repulsion modeled by nonlinear diffusion and attraction modeled by nonlocal interaction, occurs. This balance leads to continuous compactly supported radially…
We consider a non-interacting one-dimensional gas accelerated by a constant and uniform external field. The energy absorbed from the field is transferred via elastic collisions to a bath of scattering obstacles. At gas-obstacle encounters…
Over the last two decades, several methods have been proposed for stabilizing the dynamics of biological populations. However, these methods have typically been evaluated using different population dynamics models and in the context of very…
Network equilibrium models represent a versatile tool for the analysis of interconnected objects and their relationships. They have been widely employed in both science and engineering to study the behavior of complex systems under various…
We study convective stability of a two-front superposition in a reaction-diffusion system. Due to the instability of the connecting equilibrium, long-range semi-strong interaction is expected between the two waves. When restricting to the…
This paper addresses analytical aspects of deterministic, continuous-time dynamical systems defined on networks. The goal is to model and analyze certain phenomena which must be framed beyond the context of networked dynamical systems,…
We consider a mixture of passive (i.e., Brownian) and active (e.g., bacterial or colloidal swimmers) particles, and analyze the stability conditions of either uniformly mixed or phase segregated steady states consisting of phases enriched…
The original Hardenberg's model of biomass patterns in arid and semi-arid regions is revisited to extend it to more general non flat regions. It is proposed a technique to study these more generalized (non-flat) regions using both a…
We consider an integro-differential model for evolutionary game theory which describes the evolution of a population adopting mixed strategies. Using a reformulation based on the first moments of the solution, we prove some analytical…
We experimentally investigate the steady states of two granular assemblies differing in their material properties and allowed to exchange volume with each other under external agitation in the vicinity of their jamming transition. We…
We propose a general population dynamics model for two seagrass species growing and interacting in two spatial dimensions. The model includes spatial terms accounting for the clonal growth characteristics of seagrasses, and coupling between…
Systems of interacting random replicators are studied using generating functional techniques. While replica analyses of such models are limited to systems with symmetric couplings, dynamical approaches as presented here allow specifically…
We report the first experimental realization of pattern formation in a spatially extended nonlinear system when the system is alternated between two states, neither of which exhibits patterning. Dynamical equations modeling the system are…
It has long been known that complex balanced mass-action systems exhibit a restrictive form of behaviour known as locally stable dynamics. This means that within each compatibility class $\mathcal{C}_{\mathbf{x}_0}$---the forward invariant…
We search for steady states in a class of fluctuating and driven physical systems that exhibit sustained currents. We find that the physical concept of a steady state, well known for systems at equilibrium, must be generalised to describe…
The random Lotka-Volterra model is widely used to describe the dynamical and thermodynamic features of ecological communities. In this work, we consider random symmetric interactions between species and analyze the strongly competitive…
This two-part paper proposes a compositional and equilibrium-free approach to analyzing power system stability. In Part I, we have established the stability theory and proposed stability conditions based on the delta dissipativity. In Part…
In this paper, we introduce a data-driven modeling approach for dynamics problems with latent variables. The state-space of the proposed model includes artificial latent variables, in addition to observed variables that can be fitted to a…
We consider the dynamics of a smart grid system characterized by widespread distributed generation and storage devices. We assume that agents are free to trade electric energy over the network and we focus on the emerging market dynamics.…
We discuss the relevance of studying ecology within the framework of Complexity Science from a statistical mechanics approach. Ecology is concerned with understanding how systems level properties emerge out of the multitude of interactions…