Related papers: Stability and selective extinction in complex mutu…
We introduce and analyze a spatial Lotka-Volterra competition model with local and nonlocal interactions. We study two alternative classes of nonlocal competition that differ in how each species' characteristics determine the range of the…
We study a variant of the cyclic Lotka-Volterra model with three-agent interactions. Inspired by a multiplayer variation of the Rock-Paper-Scissors game, the model describes an ideal ecosystem in which cyclic competition among three species…
A classic measure of ecological stability describes the tendency of a community to return to equilibrium after small perturbation. While many advances show how the network structure of these communities severely constrains such tendencies,…
The dynamics of species' densities depend both on internal and external variables. Internal variables include frequencies of individuals exhibiting different phenotypes or living in different spatial locations. External variables include…
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…
Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…
The degree distribution is a key statistical indicator in network theory, often used to understand how information spreads across connected nodes. In this paper, we focus on non-growing networks formed through a rewiring algorithm and…
A metapopulations network is a multi-patch habitat system, where populations live and interact in the habitat patches, and individuals disperse from one patch to the other via dispersal connections. The loss of dispersal connections among…
In this paper exponential stability of nonlinear fractional order stochastic system with Poisson jumps is studied in finite dimensional space. Existence and uniqueness of solution, stability and exponential stability results are established…
We analyze ecological systems that are influenced by random environmental fluctuations. We first provide general conditions which ensure that the species coexist and the system converges to a unique invariant probability measure (stationary…
We consider the classical problem of optimal portfolio construction with the constraint that no short position is allowed, or equivalently the valid equilibria of multispecies Lotka-Volterra equations with self-regulation in the special…
In the last years, a remarkable theoretical effort has been made in order to understand stability and complexity in ecological communities. The non-random structures of real ecological interaction networks has been recognized as one key…
Plant-pollinator mutualistic networks are asymmetric in their interactions: specialist plants are pollinated by generalist animals, while generalist plants are pollinated by a broad involving specialists and generalists. It has been…
We study a parabolic Lotka-Volterra type equation that describes the evolution of a population structured by a phenotypic trait, under the effects of mutations and competition for resources modelled by a nonlocal feedback. The limit of…
Understanding the behaviors of ecological systems is challenging given their multi-faceted complexity. To proceed, theoretical models such as Lotka-Volterra dynamics with random interactions have been investigated by the dynamical…
When four species compete stochastically in a cyclic way, the formation of two teams of mutually neutral partners is observed. In this paper we study through numerical simulations the extinction processes that can take place in this system…
We present an explicit unified stochastic model of fluctuations in population size due to random birth, death, density-dependent competition and environmental fluctuations. Stochastic dynamics provide insight into small populations,…
Ecological trade-offs between species are often invoked to explain species coexistence in ecological communities. However, few mathematical models have been proposed for which coexistence conditions can be characterized explicitly in terms…
This paper is devoted to the stability analysis of an n species Lotka-Volterra system with discrete and distributed delays. Stochastic perturbations to the parameters of the model are allowed. Sufficient conditions for the almost sure…
We investigate spatially inhomogeneous versions of the stochastic Lotka-Volterra model for predator-prey competition and coexistence by means of Monte Carlo simulations on a two-dimensional lattice with periodic boundary conditions. To…