Related papers: Competitive-cooperative models with various diffus…
In this paper, the global dynamics of two-species Lotka-Volterra competition models with nonlocal dispersals is studied. Under the assumption that dispersal kernels are symmetric, we prove that except for very special situations, local…
Differential diffusion is a source of instability in population dynamics systems when species diffuse with different rates. Predator-prey systems show this instability only under certain specific conditions, usually requiring Holling-type…
In this work, we consider the spatial-temporal multi-species competition model. A mathematical model is described by a coupled system of nonlinear diffusion-reaction equations. We use a finite volume approximation with semi-implicit time…
We study a class of elliptic competition-diffusion systems of long range segregation models for two and more competing species. The existence and uniqueness of the solution are shown. We prove that as the competition rate goes to infinity…
A central model in theoretical ecology considers the competition of a range of species for a broad spectrum of resources. Recent studies have shown that essentially two different outcomes are possible. Either the species surviving…
Mixed dispersal syndromes have historically been regarded as bet-hedging mechanisms that enhance survival in unpredictable environments, ensuring that some propagules stay in the maternal environment while others can potentially colonize…
The global dynamics of the two-species Lotka-Volterra competition patch model with asymmetric dispersal is classified under the assumptions of weak competition and the weighted digraph of the connection matrix is strongly connected and…
Recently, J.-S. Guo, C.-H. Wu (Nonlinearity, 28(2015), 1-27) and C.-H. Wu (J. Differential Equations, 259(3)(2015), 873-897) studied a two-species competition-diffusion model with two free boundaries. The existence, uniqueness and long time…
In this paper, we consider the diffusive competition problem with a free boundary and sign-changing intrinsic growth rate in heterogeneous time-periodic environment, consisting of an invasive species with density $u$ and a native species…
The current paper is concerned with the existence of spreading speeds and linear determinacy for two species competition systems with nonlocal dispersal in time and space periodic habitats. The notion of spreading speed intervals for such a…
We investigate how initial and boundary conditions influence the competition dynamics and outcome in dispersal-structured populations. The study is carried out through numerical modeling of the heterogeneous Brownian bugs model, in which…
Cyclic, nonhierarchical interactions among biological species represent a general mechanism by which ecosystems are able to maintain high levels of biodiversity. However, species coexistence is often possible only in spatially extended…
Savannas are characterized by a discontinuous tree layer superimposed on a continuous layer of grass. Identifying the mechanisms that facilitate this tree-grass coexistence has remained a persistent challenge in ecology and is known as the…
This paper aims at understanding the longtime behaviors of a reducible cooperative system with nonlocal diffusions and different free boundaries, describing the interactions of two mutually beneficial species. Compared with the irreducible…
A simple cellular automata model for a two-group war over the same territory is presented. It is shown that a qualitative advantage is not enough for a minority to win. A spatial organization as well a definite degree of aggressiveness are…
We consider stochastic growth models to represent population subject to catastrophes. We analyze the subject from different set ups considering or not spatial restrictions, whether dispersion is a good strategy to increase the population…
This paper is concerned with some spreading properties of monostable Lotka--Volterra two-species competition--diffusion systems when the initial values are null or exponentially decaying in a right half-line. Thanks to a careful…
In this work, we investigate an intriguing and prevalent phenomenon of diffusion models which we term as "consistent model reproducibility": given the same starting noise input and a deterministic sampler, different diffusion models often…
We present a simple model of adaptive radiations in evolution based on species competition. Competition is found to promote species divergence and branching, and to dampen the net species production. In the model simulations, high taxonomic…
The rate of adoption of new information depends on reinforcement from multiple sources in a way that often cannot be described by simple contagion processes. In such cases, contagion is said to be complex. Complex contagion happens in the…