Related papers: Feasibility and stability in large Lotka Volterra …
We investigate the Lotka-Volterra model for predator-prey competition with a finite carrying capacity that varies periodically in time, modeling seasonal variations in nutrients or food resources. In the absence of time variability, the…
There is an growing interest in using Large Language Models (LLMs) in multi-agent systems to tackle interactive real-world tasks that require effective collaboration and assessing complex situations. Yet, we still have a limited…
We study the Lotka--Volterra system from the perspective of computational algebraic geometry, focusing on equilibria that are both feasible and stable. These conditions stratifies the parameter space in $\mathbb{R}\times\mathbb{R}^{n\times…
This work investigated the stability and asymptotic behavior of some Lotka Volterra type models. We used the Liapunov method which consists in analyzing the stability of systems of ordinary differential equations (ODEs) around the…
Empirical observations show that ecological communities can have a huge number of coexisting species, also with few or limited number of resources. These ecosystems are characterized by multiple type of interactions, in particular…
Empirical observations show that ecological communities can have a huge number of coexisting species, also with few or limited number of resources. These ecosystems are characterized by multiple type of interactions, in particular…
We compute the typical number of equilibria of the Generalized Lotka-Volterra equations describing species-rich ecosystems with random, non-reciprocal interactions using the replicated Kac-Rice method. We characterize the…
Ecological resilience refers to the ability of a system to retain its state when subject to state variables perturbations or parameter changes. While understanding and quantifying resilience is crucial to anticipate the possible regime…
Dynamical properties of numerically approximated discrete systems may become inconsistent with those of the corresponding continuous-time system. We present a qualitative analysis of the dynamical properties of two species Lotka-Volterra…
We consider two dimensional Lotka-Volterra systems in fluctuating environment. Relying on recent results on stochastic persistence and piecewise deterministic Markov processes, we show that random switching between two environments both…
We study the equilibrium phases of a generalized Lotka-Volterra model characterized by a species interaction matrix which is random, sparse and symmetric. Dynamical fluctuations are modeled by a demographic noise with amplitude proportional…
Inferring microbial community structure based on temporal metagenomics data is an important goal in microbiome studies. The deterministic generalized Lotka-Volterra differential (GLV) equations have been used to model the dynamics of…
In Human-Robot Collaboration, the robot operates in a highly dynamic environment. Thus, it is pivotal to guarantee the robust stability of the system during the interaction but also a high flexibility of the robot behavior in order to…
Large vision-language models (VLMs) such as GPT-4 have achieved unprecedented performance in response generation, especially with visual inputs, enabling more creative and adaptable interaction than large language models such as ChatGPT.…
The Lotka-Volterra model reflects real ecological interactions where species compete for limited resources, potentially leading to coexistence, dominance of one species, or extinction of another. Comprehending the mechanisms governing these…
Random matrix theory (RMT) provides a successful model for quantum systems, whose classical counterpart has a chaotic dynamics. It is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Last decade witnessed…
Over fifty years ago, Robert May applied random matrix theory to show that as ecological systems grow in size, stability decreases. What emerged from this and the critique that followed was decades of what has been called the…
In the study of disordered systems, one often chooses a matrix of independent identically distributed interaction coefficients to represent the quenched random couplings between components, perhaps with some symmetry constraint or…
We study the effect of speciation, i.e. the introduction of new species through evolution into communities, in the setting of predator-prey systems. Predator-prey dynamics is classically well modeled by Lotka-Volterra equations, also when…
Real ecosystems are characterized by sparse and asymmetric interactions, posing a major challenge to theoretical analysis. We introduce a new method to study the generalized Lotka-Volterra model with stochastic dynamics on sparse graphs. By…