Interspecific Competition Rate Research Articles

Short note on a solution with large amplitude for the limiting system arising from the competition-diffusion system

This paper is concerned with positive solutions of the limiting system arising from the Shigesada–Kawasaki–Teramoto model with large interspecific competition rate. It has previously been suggested that the limiting system has positive solutions with large amplitude for a certain value of parameters. As a first step, the purpose of this paper is to discuss the precise spatial profile of such solutions by employing formal calculations by the singular perturbation technique.

Short note on the position of bifurcation points for the limiting system arising from the two competing species model

In this paper, we treat the competition-diffusion system with nonlinear diffusion term, which was proposed by Sigesada, Kawasaki and Teramoto in 1979 to model the segregation of interacting species, and discuss the bifurcation structure of nonnegative solution for the limiting system arising from the competition-diffusion system as the interspecific competition rate tends to $ +\infty $. To do this, we employ the comparison principle and the property of the Bessel function, and study the position of bifurcation points, at which a nonconstant solution bifurcates from the constant solution, for the limiting system.

Spatial segregation limit of competition systems and free boundary problems

We consider a PDE/ODE system for two pairs of competing species and study the spatial segregation limit as the interspecific competition rate tends to infinity. We show that the limiting problem is a one‐phase Stefan problem for nonlinear diffusion equations.

On the Structure of Positive Solutions for the Shigesada–Kawasaki–Teramoto Model with Large Interspecific Competition Rate

In this paper, we treat the competition-diffusion system with nonlinear diffusion term, which was proposed by Shigesada et al. [1979], and discuss the bifurcation structure of positive solution for the system when the interspecific competition rate is sufficiently large. To do this, we derive two kinds of limiting systems as the interspecific competition rate tends to infinity, and study the bifurcation structure of positive solution for each limiting system by employing the comparison principle and the bifurcation theory.

The survival analysis of a stochastic Lotka-Volterra competition model with a coexistence equilibrium.

In this paper, we propose and analyze a two-species Lotka-Volterra competition model with random perturbations that relate to the inter-specific competition rates and the coexistence equilibrium of the corresponding deterministic system. The stochasticity in inter-specific competition (between species) is more important than that in intra-specific competition (within species). We pose two assumptions and then obtain su cient conditions for coexistence and for competitive exclusion respectively, and find that small random perturbations will not destroy the dynamic behaviors of the corresponding deterministic system. Moreover, if one species goes extinct, the convergence rate to zero is obtained by investigating the Lyapunov exponent. Finally, we provide several numerical examples to illustrate our mathematical results.

Global asymptotic stability of a Lotka–Volterra competition model with stochasticity in inter-specific competition

Global asymptotic stability of a Lotka–Volterra competition model with stochasticity in inter-specific competition

Competition in periodic media: II – Segregative limit of pulsating fronts and “Unity is not Strength”-type result

Competition in periodic media: II – Segregative limit of pulsating fronts and “Unity is not Strength”-type result

On the asymptotic growth of positive solutions to a nonlocal elliptic blow-up system involving strong competition

On the asymptotic growth of positive solutions to a nonlocal elliptic blow-up system involving strong competition

Spatial Segregation Limit of a Quasilinear Competition-Diffusion System

The aim of this paper is to investigate a Volterra-Lotka competition model of quasilinear parabolic equations with large interaction. Some existence, uniqueness and convergence results for the system are given. Also investigated is its spatial segregation limit when the interspecific competition rates become large. We show that the limit problem is similar to a free boundary problem.

THE EXISTENCE AND ASYMPTOTIC BEHAVIOR OF PERIODIC SOLUTIONS TO A QUASILINEAR PARABOLIC SYSTEM

In this paper, we investigate the existence, stability and global attractivity of T-periodic solutions for a class of quasilinear parabolic equations under Robin boundary conditions. We obtain that periodic solutions exist if the inter-specific competition rates are weak. The numerical simulations are also presented to illustrate our result.

The spatial behavior of a competition–diffusion–advection system with strong competition

The spatial behavior of a competition–diffusion–advection system with strong competition

Singular limit of a competition–diffusion system with large interspecific interaction

Singular limit of a competition–diffusion system with large interspecific interaction

The asymptotic periodicity in a Schoener’s competitive model

The asymptotic periodicity in a Schoener’s competitive model

On the long term spatial segregation for a competition–diffusion system

We investigate the long term behavior for a class of competition–diffusion systems of Lotka–Volterra type for two competing species in the case of low regularity assumptions on the data. Due to the coupling that we consider the system cannot be reduced to a single equation yielding uniform estimates with respect to the inter-specific competition rate parameter. Moreover, in the particular but meaningful case of initial data with disjoint support and Dirichlet boundary data which are time-independent, we prove that as the competition rate goes to infinity the solution converges, along with suitable sequences, to a spatially segregated state satisfying some variational inequalities.

Spatial segregation limit of a competition-diffusion system with Dirichlet boundary conditions

Spatial segregation limit of a competition-diffusion system with Dirichlet boundary conditions

Harmless and Profitless Delays in Discrete Competitive Lotka–Volterra Systems

Recently, time-delayed discrete population dynamical systems have received much attention. Many authors are interested in studying the effects of time-delays on the dynamical behaviors of discrete systems. Among them, Saito et al. [Y. Saito, W. Ma and T. Hara (2001). Necessary and sufficient condition for permanence of a Lotka–Volterra discrete system with delays. J. Math. Anal. Appl., 256, 162–174; Y. Saito, T. Hara and W. Ma (2002). Harmless delays for permanence and impersistence of Lotka–Volterra discrete predator–prey system. Nonlinear Analysis, 50, 703–715.], Tang and Xiao [S. Tang and Y. Xiao (2001). Permanence in Kolmogorov-Type systems of delay difference equations. J. Diff. Eqns. Appl., 7, 1–15.] have considered the two-species Lotka–Volterra discrete system with time-delays, and they conclude that time-delays therein are harmless for permanence. How will time-delays affect the dynamical behaviors of the general Lotka–Volterra discrete systems? In this article, we discuss a general n-species discrete competitive Lotka–Volterra system with delayed density dependence and delayed interspecific competition. We obtain some new results about the effect of time-delays on permanence, extinction and balancing survival. We conclude that under some conditions, the inclusion, exclusion and change of time-delays do not affect the conditions for the permanence, extinction and balancing survival of species. We also find that time-delays are harmless for both the permanence and balancing survival of species, in addition to being profitless to the extinction of species. In particular, when n = 2, the extinction and permanence of this system are corresponded to some inequalities that only involve the coefficients therein. Importantly, permanence and extinction in this two-species system are determined only by three elements: growth rate, density dependence and interspecific competition rate.

Segregating partition problem in competition-diffusion systems

We consider a reaction-diffusion system to describe the interaction of three competing species which move by diffusion in R2, under the situation where all of the diffusion rates are small and all of the inter-specific competition rates are large. The resulting system possesses three locally stable spatially constant equilibria, each of which implies that only one of the competing species survive and the other two are extinct. Since the diffusion rates are small, internal layer regions appear as sharp interfaces with triple junctions, which generally divide the whole plane into three different regions occupied by only one of the species. The dynamics of interfaces as well as triple junctions are numerically studied. More specifically, assuming that three competing species are almost equal in competitive strength, we derive an angle condition between any neighboring interfaces at triple junctions by formal asymptotic analysis. Furthermore, for more general cases, we numerically study the dynamics of segregating patterns of three competing species from interfacial view points.