相关论文: Equilibrium in a large Lotka-Volterra system with …
A possible approach to description of the non equilibrium system has been proposed. Based on the Fokker-Plank equation in term of energy for non equilibrium distribution function of macroscopical system was obtained the stationary solution…
We study a diffusive Lotka-Volterra competition system with advection under Neumann boundary conditions. Our system models a competition relationship that one species escape from the region of high population density of their competitors in…
We analyze the role of the Allee effect, a positive correlation between population density and mean individual fitness, for ecological communities formed by a large number of species. Our study is performed using the generalized…
This paper provides global attractivity results for the interior equilibrium point of a general Lotka-Volterra system with no restriction on the dimension of the system and with no special structure or properties of the interaction matrix.…
Large systems of linear equations are ubiquitous in science. Quite often, e.g. when considering population dynamics or chemical networks, the solutions must be non-negative. Recently, it has been shown that large systems of random linear…
In this note, we study the long time behavior of Lotka-Volterra systems whose coefficients vary randomly. Bena{\"i}m and Lobry (2015) recently established that randomly switching between two environments that are both favorable to the same…
The rapid advancement of environmental sequencing technologies, such as metagenomics, has significantly enhanced our ability to study microbial communities. The eubiotic composition of these communities is crucial for maintaining ecological…
Stochastic differential equations have proved to be a valuable governing framework for many real-world systems which exhibit ``noise'' or randomness in their evolution. One quality of interest in such systems is the shape of their…
In a diverse population, where many species are present, competitors can fight for surviving at individual and collective levels. In particular, species, which would beat each other individually, may form a specific alliance that ensures…
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 consider evolution equations of the Lotka-Volterra type, and elucidate especially their formulation as canonical Hamiltonian systems. The general conditions under which these equations admit several conserved quantities…
Ecological interaction networks are rarely homogeneous: species naturally form communities with distinct interaction structures, resulting in block-structured variance and correlation profiles in the interaction matrix. We study the…
We study the Lotka--Volterra system from the perspective of computational algebraic geometry, focusing on equilibria that are both feasible and stable. These conditions stratifies the parameter space in $\mathbb{R}\times\mathbb{R}^{n\times…
The paper deals with a multiple species Lotka-Volterra model with infinite distributed delays and feedback controls, for which we assume a weak form of diagonal dominance of the instantaneous negative intra-specific terms over the infinite…
Q-conditional symmetries of the classical Lotka-Volterra system in the case of one space variable are completely described and a set of such symmetries in explicit form is constructed. The relevant non-Lie ans\"atze to reduce the classical…
The nonequilibrium phase transition in a system of diffusing, coagulating particles in the presence of a steady input and evaporation of particles is studied. The system undergoes a transition from a phase in which the average number of…
The noise-induced pattern formation in a population dynamical model of three interacting species in the coexistence regime is investigated. A coupled map lattice of Lotka-Volterra equations in the presence of multiplicative noise is used to…
This paper presents new analytical results for a class of nonlinear parabolic systems of partial different equations with small cross-diffusion which describe the macroscopic dynamics of a variety of large systems of interacting particles.…
Owing to the analogies between the problem of wealth redistribution with taxation in a multi-agent society, we introduce and discuss a kinetic model describing the statistical distributions in time of the sizes of groups of biological…
This work investigated the stability and asymptotic behavior of some Lotka Volterra type models. We used the Liapunov method which consists in analyzing the stability of systems of ordinary differential equations (ODEs) around the…