Related papers: Well-mixed Lotka-Volterra model with random strong…
Stochastic, spatially extended models for predator-prey interaction display spatio-temporal structures that are not captured by the Lotka-Volterra mean-field rate equations. These spreading activity fronts reflect persistent correlations…
This paper is concerned with a diffusive Lotka-Volterra type competition system with a free boundary in one space dimension. Such a system may be used to describe the invasion of a new species into the habitat of a native competitor. We…
The study of ecological systems is gaining momentum in modern scientific research, driven by an abundance of empirical data and advancements in bioengineering techniques. However, a full understanding of their dynamical and thermodynamical…
In this paper we are investigating the long time behaviour of the solution of a mutation competition model of Lotka-Volterra's type. Our main motivation comes from the analysis of the Lotka-Volterra's competition system with mutation which…
We investigate the spreading behavior of two invasive species modeled by a Lotka-Volterra diffusive competition system with two free boundaries in a spherically symmetric setting. We show that, for the weak-strong competition case, under…
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…
Systems of interacting species, such as biological environments or chemical reactions, are often described mathematically by sets of coupled ordinary differential equations. While a large number $\beta$ of species may be involved in the…
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…
We study a normalized two dimensional competitive Lotka$-$Volterra system describing the interaction between state power and society power. Restricting attention to the positively invariant domain $[0,1]^2$, the analysis focuses on interior…
We analyze the long term behavior of interacting populations which can be controlled through harvesting. The dynamics is assumed to be discrete in time and stochastic due to the effect of environmental fluctuations. We present extinction…
Statistical mechanics of relative species abundance (RSA) patterns in biological networks is presented. The theory is based on multispecies replicator dynamics equivalent to the Lotka-Volterra equation, with diverse interspecies…
Our earlier work in \cite{nguyen2022population} shows that concentrating the resources on the upstream end tends to maximize the total biomass in a metapopulation model for a stream species. In this paper, we continue our research direction…
Population dynamics of a competitive two-species system under the influence of random events are analyzed and expressions for the steady-state population mean, fluctuations, and cross-correlation of the two species are presented. It is…
In this paper, we investigate a two-species Lotka-Volterra competition patch model in a Y-shaped river network, where the two species are assumed to be identical except for their random and directed movements. We show that competition…
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 influence of spatially varying reaction rates on a spatial stochastic two-species Lotka-Volterra lattice model for predator-prey interactions using two-dimensional Monte Carlo simulations. The effects of this quenched…
We study the dynamics of the generalized Lotka-Volterra model with a network structure. Performing a high connectivity expansion for graphs, we write down a mean-field dynamical theory that incorporates degree heterogeneity. This allows us…
Coevolutionary dynamics is investigated in chemical catalysis, biological evolution, social and economic systems. The dynamics of these systems can be analyzed within the unifying framework of evolutionary game theory. In this Letter, we…
We show how highly-diverse ecological communities may display persistent abundance fluctuations, when interacting through resource competition and subjected to migration from a species pool. This turns out to be closely related to the ratio…
A new model ecosystem consisting of many interacting species is introduced. The species are connected through a random matrix with a given connectivity. It is shown that the system is organized close to a boundary of marginal stability in…