Related papers: On Rank Driven Dynamical Systems
We introduce the standard distribution width of fitness to characterize the global and individual features of a ecosystem in the Bak-Sneppen evolution model. Through tracking this quantity in evolution, a different hierarchy of avalanche…
The $NK$ model, introduced by Kauffman, Levin, and Weinberger, is a random field used to describe the fitness landscape of certain species with $N$ genetic loci, each interacting with $K$ others. The model has wide applications in…
Discrete time, spatially extended models play an important role in ecology, modelling population dynamics of species ranging from micro-organisms to birds. An important question is how 'bottom up', individual-based models can be…
We model a system of networking agents that seek to optimize their centrality in the network while keeping their cost, the number of connections they are participating in, low. Unlike other game-theory based models for network evolution,…
This paper describes a formalization of agent-based models (ABMs) as random walks on regular graphs and relates the symmetry group of those graphs to a coarse-graining of the ABM that is still Markovian. An ABM in which $N$ agents can be in…
The behavior of heterogeneous multi-agent systems is studied when the coupling matrices are possibly all different and/or singular, that is, its rank is less than the system dimension. Rank-deficient coupling allows exchange of limited…
In this article we investigate the phase transition phenomena that occur in a model of self-organisation through body-attitude coordination. Here, the body-attitude of an agent is modelled by a rotation matrix in $\mathbb{R}^3$ as in…
We study a model of learning on social networks in dynamic environments, describing a group of agents who are each trying to estimate an underlying state that varies over time, given access to weak signals and the estimates of their social…
Distribution shifts have long been regarded as troublesome external forces that a decision-maker should either counteract or conform to. An intriguing feedback phenomenon termed decision dependence arises when the deployed decision affects…
See the updated version arXiv:nlin/0111028.
This paper is concerned with a mathematical model of competition for resource where species consume noninteracting resources. This system of differential equations is formally obtained by renormalizing the MacArthur's competition model at…
Many natural systems, such as neurons firing in the brain or basketball teams traversing a court, give rise to time series data with complex, nonlinear dynamics. We can gain insight into these systems by decomposing the data into segments…
We consider change-point tests based on rank statistics to test for structural changes in long-range dependent observations. Under the hypothesis of stationary time series and under the assumption of a change with decreasing change-point…
An agent-based model is proposed for analyzing the dynamics that arise from interactions within social networks, analyzing the individual behavior of each profile. Said model considers a simplified construction of a social network while…
While the use of spatial agent-based and individual-based models has flourished across many scientific disciplines, the complexities these models generate are often difficult to manage and quantify. This research reduces population-driven,…
An emerging paradigm proposes that neural computations can be understood at the level of dynamical systems that govern low-dimensional trajectories of collective neural activity. How the connectivity structure of a network determines the…
We propose a family of models to study the evolution of ties in a network of interacting agents by reinforcement and penalization of their connections according to certain local laws of interaction. The family of stochastic dynamical…
In nature self-organized systems as flock of birds, school of fishes or herd of sheeps have to deal with the presence of external agents such as predators or leaders which modify their internal dynamic. Such situations take into account a…
We initiate the study of game dynamics in the population protocol model: $n$ agents each maintain a current local strategy and interact in pairs uniformly at random. Upon each interaction, the agents play a two-person game and receive a…
We consider a model for which every site of $\mathbb{N}$ is assigned a fitness in $[0,1]$. At every discrete time all the sites are updated and each site samples a uniform on $[0,1]$, independently of everything else. At every discrete time…