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We analyze the nonlinear relaxation of a complex ecosystem composed of many interacting species. The ecological system is described by generalized Lotka-Volterra equations with a multiplicative noise. The transient dynamics is studied in…
In this paper, we introduce a general framework to quantify dissimilarities between generalized Lotka-Volterra dynamical processes, ranging from classical predator-prey systems to multispecies communities interacting on networks. The…
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…
In this work, we explore the dynamics of species abundances within ecological communities using the Generalized Lotka-Volterra (GLV) model. At variance with previous approaches, we present an analysis of stochastic GLV dynamics with…
In this paper we study the long term dynamics of two prey species and one predator species. In the deterministic setting, if we assume the interactions are of Lotka-Volterra type (competition or predation), the long term behavior of this…
To describe population dynamics, it is crucial to take into account jointly evolution mechanisms and spatial motion. However, the models which include these both aspects, are not still well-understood. Can we extend the existing results on…
We present new theoretical and empirical results on the probability distributions of species persistence times in natural ecosystems. Persistence times, defined as the timespans occurring between species' colonization and local extinction…
Spatial extent is a complicating factor in mathematical biology. The possibility that an action at point A cannot immediately affect what happens at point B creates the opportunity for spatial nonuniformity. This nonuniformity must change…
In this work, we consider a system of differential equations modeling the dynamics of some populations of preys and predators, moving in space according to rapidly oscillating time-dependent transport terms, and interacting with each other…
Some quantities in the reaction-diffusion models from cellular biology or ecology depend on the spatial average of density functions instead of local density functions. We show that such nonlocal spatial average can induce instability of…
Noise, through its interaction with the nonlinearity of the living systems, can give rise to counter-intuitive phenomena such as stochastic resonance, noise-delayed extinction, temporal oscillations, and spatial patterns. In this paper we…
Reaction-diffusion systems with a Lotka-Volterra-type reaction term, also known as competition-diffusion systems, have been used to investigate the dynamics of the competition among $m$ ecological species for a limited resource necessary to…
We investigate the Multiple Equilibria phase of generalized Lotka-Volterra dynamics with random, non-reciprocal interactions. We compute the topological complexity of equilibria, which quantifies how rapidly the number of equilibria of the…
The distributions of species lifetimes and species in space are related, since species with good local survival chances have more time to colonize new habitats and species inhabiting large areas have higher chances to survive local…
We study a model ecosystem by means of dynamical techniques from disordered systems theory. The model describes a set of species subject to competitive interactions through a background of resources, which they feed upon. Additionally…
We consider a couple of models for the dynamics of the populations of two interacting species, inspired by Lotka-Volterra's classical equations. The novelty of this work is that the interaction terms are non local and the interaction occurs…
Ecosystems with a large number of species are often modelled as Lotka-Volterra dynamical systems built around a large random interaction matrix. Under some known conditions, a global equilibrium exists and is unique. In this article, we…
This paper studies the spreading dynamics of a high-dimensional strong competition Lotka-Volterra system where two species initially occupy disjoint measurable (possibly unbounded) subsets in $\mathbb{R}^N$, which are called initial…
We study the general properties of stochastic two-species models for predator-prey competition and coexistence with Lotka-Volterra type interactions defined on a $d$-dimensional lattice. Introducing spatial degrees of freedom and allowing…
Understanding under what conditions interacting populations, whether they be plants, animals, or viral particles, coexist is a question of theoretical and practical importance in population biology. Both biotic interactions and…