Related papers: Rock-paper-scissors models with a preferred mobili…
For years, a main focus of ecological research has been to better understand the complex dynamical interactions between species which comprise food webs. Using the connectance properties of a widely explored synthetic food web called the…
In this paper, we mainly consider the speed selection problem for the classical Lotka-Volterra competition system. For the first time, we propose a sufficient and necessary condition for this long-standing problem from a new point of view.…
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…
We are interested in the long time behavior of a two-type density-dependent biological population conditioned to non-extinction, in both cases of competition or weak cooperation between the two species. This population is described by a…
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…
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…
The spatial rock-paper-scissors ecosystem, where three species interact cyclically, is a model example of how spatial structure can maintain biodiversity. We here consider such a system for a broad range of interaction rates. When one…
We describe pattern formation in ecological systems using a version of the classical Lotka-Volterra model characterized by a spatial scale which controls the predator-prey interaction range. Analytical and simulational results show that…
Recurrence plots and their associated quantifiers provide a robust framework for detecting and characterising complex patterns in non-linear time-series. In this paper, we employ recurrence quantification analysis to investigate the…
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…
This study uses the Lotka Volterra Predator-Prey model to offer a notion of piecewise patterns for the various piecewise derivatives. Using the piecewise derivatives, we produced numerical solutions that are referred to as the…
In this paper, we consider the inverse problem of determining the coefficients of interaction terms within some Lotka-Volterra models, with support from boundary observation of its non-negative solutions. In the physical background, the…
The forces which drive growth, development, survival and change within an ecological system involving a predator and prey specie are not easily addressed in the field. To better understand the dynamics in the system, ecologists have turned…
We study the cyclic dominance of three species in two-dimensional constrained Newman-Watts networks with a four-state variant of the rock-paper-scissors game. By limiting the maximal connection distance $R_{max}$ in Newman-Watts networks…
We have analyzed the interplay between noise and periodic modulations in a classical Lotka-Volterra model of two-species competition. We have found that the consideration of noise changes drastically the behavior of the system and leads to…
Using Monte Carlo simulations we study a lattice model of a prey-predator system. We show that in the three-dimensional model populations of preys and predators exhibit coherent periodic oscillations but such a behaviour is absent in…
A five-species predator-prey model is studied on a square lattice where each species has two prey and two predators on the analogy to the Rock-Paper-Scissors-Lizard-Spock game. The evolution of the spatial distribution of species is…
We consider a Lotka-Volterra food chain model with possibly intra-specific competition in a stochastic environment represented by stochastic differential equations. In the non-degenerate setting, this model has already been studied by A.…
Cyclic dominant systems, like rock-paper-scissors game, are frequently used to explain biodiversity in nature, where mobility, reproduction and intransitive competition are on stage to provide the coexistence of competitors. A significantly…
We study generalised rock-paper-scissors models with an arbitrary odd number N \geq 5 of species, among which n are weak, with 2 \leq n \leq (N-1)/2. Because of the species' weakness, the probability of individuals conquering territory in…