Related papers: Invariance of Competition Outcomes in Hypergraph C…
We show that a general class of social impact models with higher-order interactions on hypergraphs can be exactly reduced to an equivalent model with pairwise interactions on a weighted projected network. This reduction is made by a mapping…
In this paper, we study in detail the structure of the global attractor for the Lotka--Volterra system with a Volterra--Lyapunov stable structural matrix. We consider the invasion graph as recently introduced in [19] and prove that its…
Higher-order interactions are increasingly recognized as a key component of ecological dynamics. However, we show that higher-order Lotka-Volterra dynamics can, in some scenarios, be accurately reproduced by effective pairwise models fitted…
Hypergraphs have been a useful tool for analyzing population dynamics such as opinion formation and the public goods game occurring in overlapping groups of individuals. In the present study, we propose and analyze evolutionary dynamics on…
This paper is devoted to the analysis of a simple Lotka-Volterra food chain evolving in a stochastic environment. It can be seen as the companion paper of Hening and Nguyen (J. of Math. Biol. `18) where we have characterized the persistence…
Many real systems are strongly characterized by collective cooperative phenomena whose existence and properties still need a satisfactory explanation. Coherently with their collective nature, they call for new and more accurate descriptions…
The global asymptotic behavior of the classical diffusive Lotka-Volterra competition model with stage structure is studied. A complete classification of the global dynamics is given for the weak competition case. It is shown that under…
Classical models for competition between two species usually predict exclusion or divergent evolution of resource exploitation. However, recent experimental data show that coexistence is possible for very similar species competing for the…
Winner-Take-All (WTA) refers to the neural operation that selects a (typically small) group of neurons from a large neuron pool. It is conjectured to underlie many of the brain's fundamental computational abilities. However, not much is…
Classical approaches to ecological stability rely on fully connected interaction models, yet real ecosystems are sparse and structured--a feature that qualitatively reshapes their collective dynamics. Here, we establish a thermodynamically…
Interactions between people are the basis on which the structure of our society arises as a complex system and, at the same time, are the starting point of any physical description of it. In the last few years, much theoretical research has…
Does an ecological community allow stable coexistence? Identifying the general principles that determine the answer to this question is a central problem of theoretical ecology. Random matrix theory approaches have uncovered the general…
We focus on the long term dynamics of "killing the winner" Lotka-Volterra models of marine communities consisting of bacteria, virus, and zooplankton. Under suitable conditions, it is shown that there is a unique equilibrium with all…
Higher-order networks have emerged as a powerful framework to model complex systems and their collective behavior. Going beyond pairwise interactions, they encode structured relations among arbitrary numbers of units through representations…
This work attempts to address adversarial robustness of deep networks by means of novel learning arguments. Specifically, inspired from results in neuroscience, we propose a local competition principle as a means of adversarially-robust…
We investigate cyclic dominance models and their extensions to both network systems and reaction-diffusion frameworks. Using linear stability analysis, we establish the relationship between the stability of synchronized states in network…
The dynamic behavior of a multiagent system in which the agent size $s_{i}$ is variable it is studied along a Lotka-Volterra approach. The agent size has hereby for meaning the fraction of a given market that an agent is able to capture…
Hebbian plasticity in winner-take-all (WTA) networks is highly attractive for neuromorphic on-chip learning, owing to its efficient, local, unsupervised, and on-line nature. Moreover, its biological plausibility may help overcome important…
A central concern of community ecology is the interdependence between interaction strengths and the underlying structure of the network upon which species interact. In this work we present a solvable example of such a feedback mechanism in…
In the study of dynamical systems on networks/graphs, a key theme is how the network topology influences stability for steady states or synchronized states. Ideally, one would like to derive conditions for stability or instability that…