Related papers: Some "counterintuitive" results in two species com…
The persistence of biodiversity of species is a challenging proposition in ecological communities in the face of Darwinian selection. The present article investigates beyond the pairwise competitive interactions and provides a novel…
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 bacterial species produce toxins that inhibit their competitors. We model this phenomenon by extending classic two-species Lotka-Volterra competition in one spatial dimension to incorporate toxin production by one species. Considering…
We study a competition-diffusion model while performing simultaneous homogenization and strong competition limits. The limit problem is shown to be a Stefan type evolution equation with effective coefficients. We also perform some numerical…
In this paper, we gives a complete classification of the global dynamics of two- species Lotka-Volterra competition models with nonlocal dispersals: where K, P represent nonlocal operators, under the assumptions that the nonlo- cal…
In this second part of the series, we investigate the uniqueness of positive fixed points of the Poincare map associated with the 3-dimensional Lotka-Volterra competition model with seasonal succession. Building on our first part of the…
Spontaneous formation of transverse patterns is ubiquitous in nonlinear dynamical systems of all kinds. An aspect of particular interest is the active control of such patterns. In nonlinear optical systems this can be used for all-optical…
We study the persistence and extinction of species in a simple food chain that is modelled by a Lotka-Volterra system with environmental stochasticity. There exist sharp results for deterministic Lotka-Volterra systems in the literature but…
In order to understand how impulsive interventions and environmental perturbations affect dynamics of competitors, we focus on a diffusive competition model with free boundaries and periodic pulses in a temporally heterogeneous environment…
We study how increasing competition, by making prizes more unequal, affects effort in contests. In a finite type-space environment, we characterize the equilibrium, analyze the effect of competition under linear costs, and identify…
This paper is concerned with the asymptotic spreading behavior of solutions of the Lotka-Volterra system with strong competition in $\mathbb{R}^{N}$. Two types of initial conditions are proposed: (C1) two species initially occupy bounded…
For classic Lotka-Volterra systems governing many interacting species, we establish an exclusion principle that rules out the existence of linearly asymptotically stable steady states in subcommunitites of communities that admit a stable…
We propose two models of the evolution of a pair of competing populations. Both are lattice based. The first is a compromise between fully spatial models, which do not appear amenable to analytic results, and interacting particle system…
May and Leonard (SIAM J. Appl. Math 1975) introduced a three-species Lotka-Volterra type population model that exhibits heteroclinic cycling. Rather than producing a periodic limit cycle, the trajectory takes longer and longer to complete…
Resource-based competition between microorganisms species in continuous culture has been studied extensively both experimentally and theoretically, mostly for bacteria through Monod and and Contois "constant yield" models, or for…
In this study, we apply two pillars of Scientific Machine Learning: Neural Ordinary Differential Equations (Neural ODEs) and Universal Differential Equations (UDEs) to the Lotka Volterra Predator Prey Model, a fundamental ecological model…
Understanding how a diversity of plants in agroecosystems affects the adaptation of pathogens in a key issue in agroecology. We analyze PDE systems describing the dynamics of adaptation of two phenotypically structured populations, under…
In this paper, we investigate a Lotka-Volterra competition-diffusion system with self-memory effects and spatial heterogeneity under Dirichlet boundary conditions. We focus on how memory strength influences the coexistence and stability of…
We study a two-dimensional process $(X, Y)$ arising as the unique nonnegative solution to a pair of stochastic differential equations driven by independent Brownian motions and compensated spectrally positive L\'evy random measures. Both…
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…