相关论文: A robust multiplicity result in a generalized diff…

In this paper we present analytical solution of a fractional order predator-prey model, where prey grows logistically and predation occurs following type II response function, by homotopy perturbation method. Numerical solutions are…

In this paper, we study two PDEs that generalize the urban crime model proposed by Short \emph{et al}. [Math. Models Methods Appl. Sci., 18 (2008), pp. 1249-1267]. Our modifications are made under assumption of the spatial heterogeneity of…

When two Turing modes interact, i.e., Turing-Turing bifurcation occurs, superposition patterns revealing complex dynamical phenomena appear. In this paper, superposition patterns resulting from Turing-Turing bifurcation are investigated in…

In this paper, a single population model with memory effect and the heterogeneity of the environment, equipped with the Neumann boundary, is considered. The global existence of a spatial nonhomogeneous steady state is proved by the method…

We perform individual-based Monte Carlo simulations in a community consisting of two predator species competing for a single prey species, with the purpose of studying biodiversity stabilization in this simple model system. Predators are…

We analyse the stability of linear dynamical systems defined on sparse, random graphs with predator-prey, competitive, and mutualistic interactions. These systems are aimed at modelling the stability of fixed points in large systems defined…

We study a simple model of a diffusing particle (the prey) that on encounter with one of a swarm of diffusing predators can either perish or be reset to its original position at the origin. We show that the survival probability of the prey…

The present paper deals with a prey-predator model with prey refuge proportion to both species and independent harvesting of each species. Our study shows that using refuge as control, it can break the limit circle of the system and reach…

We present new a stability result for periodic solutions of the periodic predator prey Lotka Volterra model, based on boundaries for the average of the coexistence states. Our result complements previous one in the literature.

Neutral theories have played a crucial and revolutionary role in fields such as population genetics and biogeography. These theories are critical by definition, in the sense that the overall growth rate of each single allele/species/type…

In this paper we provide an elementary proof of the existence of canard solutions for a class of singularly perturbed predator-prey planar systems in which there occurs a transcritical bifurcation of quasi steady states. The proof uses a…

The introduction of stochasticity into continuous ecological models frequently relies on phenomenological, diagonal diffusion terms that lack a rigorous microscopic basis. We demonstrate that this standard practice fundamentally…

The rock-paper-scissor game -- which is characterized by three strategies R,P,S, satisfying the non-transitive relations S excludes P, P excludes R, and R excludes S -- serves as a simple prototype for studying more complex non-transitive…

The current paper is concerned with pointwise persistence in full chemotaxis models with local as well as nonlocal time and space dependent logistic source in bounded domains. We first prove the global existence and boundedness of…

A diffusive epidemic model with an infection-dependent recovery rate is formulated in this paper. Multiple constant steady states and spatially homogeneous periodic solutions are first proven by bifurcation analysis of the reaction…

In order to model real ecological systems one has to consider many species that interact in complex ways. However, most of the recent theoretical studies have been restricted to few species systems with rather trivial interactions. The few…

Simulation of stochastic spatially-extended systems is a challenging problem. The fundamental quantities in these models are individual entities such as molecules, cells, or animals, which move and react in a random manner. In big systems,…

Consider the coupling of $2$ evolution equations, each generating a global process. We prove that the resulting system generates a new global process. This statement can be applied to differential equations of various kinds. In particular,…

This paper investigates the dynamical behaviors of a Holling type I Leslie-Gower predator-prey model where the predator exhibits an Allee effect and is subjected to constant harvesting. The model demonstrates three types of equilibrium…

We study the existence and stability of propagating fronts in Meinhardt's multivariable reaction-diffusion model of branching in one spatial dimension. We identify a saddle-node-infinite-period (SNIPER) bifurcation of fronts that leads to…