Related papers: Stability and selective extinction in complex mutu…
Non-autonomous differential equations exhibit a highly intricate dynamics, and various concepts have been introduced to describe their qualitative behavior. In general, it is rare to obtain time dependent invariant compact attracting sets…
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…
In complex ecological communities, species may self-organize into clusters or clumps where highly similar species can coexist. The emergence of such species clusters can be captured by the interplay between neutral and niche theories. Based…
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…
This paper systematically investigates the optimal harvesting of a stochastic Lotka-Volterra competition model with periodic coefficients. Sufficient conditions for the extinction and persistence in the time average of each species are…
This article is concerned with a mutualism ecological model with stochastic perturbations. the local existence and uniqueness of a positive solution are obtained with positive initial value, and the asymptotic behavior to the problem is…
Mutualistic networks provide a powerful way to describe and analyse plant-pollinator communities and their structure over time. While these networks capture the complex interdependencies that link population fates across the season, they…
We show that spatial extensions of many-species population dynamics models, such as the Lotka-Volterra model with random interactions we focus on in this work, generically exhibit scale-free correlation functions of population sizes in the…
The statistical properties of an ecosystem composed of species interacting via pairwise, random interactions and deterministic, concentration limiting self-interaction are studied analytically with tools of equilibrium statistical mechanics…
Stability is a desirable property of complex ecosystems. If a community of interacting species is at a stable equilibrium point then it is able to withstand small perturbations to component species' abundances without suffering adverse…
The dynamical mechanisms that can stabilize the coexistence of species (or strategies) are of substantial interest for the maintenance of biodiversity and in sociobehavioural dynamics. We investigate the mean extinction time in the…
Species-rich ecosystems often exhibit multiple stable states with distinct species compositions. Yet, the factors determining the likelihood of each state's occurrence remain poorly understood. Here, we characterize and explain the…
We study the dynamics of a second-order difference equation that is derived from a planar Ricker model of two-stage (e.g. adult, juvenile) biological populations. We obtain sufficient conditions for global convergence to zero in the…
A non-periodic version of the one-predator two-prey system model presented in [L.T.H. Nguyen, Q.H. Ta, T.V. T\d{a}, Existence and stability of periodic solutions of a Lotka-Volterra system, SICE International Symposium on Control Systems,…
How do interactions between species influence their spatial distribution in an ecosystem? To answer this question, we introduce a spatially-extended ecosystem of Generalized Lotka-Volterra type, where species can diffuse and interactions…
Ecological communities with many species can be classified into dynamical phases. In systems with all-to-all interactions, a phase where a fixed point is always reached and a dynamically-fluctuating phase have been found. The dynamics when…
Lotka-Volterra (LV) equations play a key role in the mathematical modeling of various ecological, biological and chemical systems. When the number of species (or, depending on the viewpoint, chemical components) becomes large, basic but…
A diffusive Lotka-Volterra competition model is considered for the combined effect of spatial dispersal and spatial variations of resource on the population persistence and exclusion. First it is shown that in a two-species system in which…
We consider a nonlinear coupled discrete-time model of population dynamics. This model describes the movement of populations within a heterogeneous landscape, where the growth of subpopulations are modelled by (possibly different) bounded…
We investigate the formation of stable ecological networks where many species share the same resource. We show that such stable ecosystem naturally occurs as a result of extinctions. We obtain an analytical relation for the number of…