Related papers: A sufficient condition on successful invasion by t…
This paper is concerned with the conditions of existence and nonexistence of traveling wave solutions (TWS) for a class of discrete diffusive epidemic models. We find that the existence of TWS is determined by the so-called basic…
In this paper we revisit the existence of traveling waves for delayed reaction diffusion equations by the monotone iteration method. We show that Perron Theorem on existence of bounded solution provides a rigorous and constructive framework…
This paper is concerned with the traveling wave solutions of an integro-difference competition system, of which the purpose is to model the coinvasion-coexistence process of two competitors with age structure. The existence of nontrivial…
We consider planar systems of predator-prey models with small predator death rate $\epsilon>0$. Using geometric singular perturbation theory and Floquet theory, we derive characteristic functions that determines the location and the…
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…
We consider an epidemic model with direct transmission given by a system of nonlinear partial differential equations and study the existence of traveling wave solutions. When the basic reproductive number of the considered model is less…
Existence, uniqueness and classification is established for plane waves supported by an irreversible reaction which is a smooth function of local reactant and product concentrations (or prey and predator populations). Rudimentary analytic…
The outcome of competition among species is influenced by the spatial distribution of species and effects such as demographic stochasticity, immigration fluxes, and the existence of preferred habitats. We introduce an individual-based model…
In this paper, we study a strongly coupled two-prey one-predator system. We first prove the unique positive equilibrium solution is globally asymptotically stable for the corresponding kinetic system (the system without diffusion) and…
In this paper, the existence of a non-trivial, positive and bounded critical traveling wave solution of a diffusive disease model, whose reaction system has infinity many equilibria, is obtained for the first time. This gives an affirmative…
The comprehension of how local interactions arise in global collective behavior is of utmost importance in both biological and physical research. Traditional agent-based models often rely on static rules that fail to capture the dynamic…
We study the spreading of families in two-dimensional multispecies predator-prey systems, in which species cyclically dominate each other. In each time step randomly chosen individuals invade one of the nearest sites of the square lattice…
This paper is devoted to investigating the effects and biological consequences of the predator-mediated apparent competition based on a two prey species (one is native and the other is invasive) and one predator model with Holling type I…
We prove existence and uniqueness of travelling waves for a reaction-diffusion system coupling a classical reaction-diffusion equation in a strip with a diffusion equation on a line. To do this we use a continuation method which leads to…
We address the problem of how the survival of cooperation in a social system depends on the motion of the individuals. Specifically, we study a model in which Prisoner's Dilemma players are allowed to move in a two-dimensional plane. Our…
We study the stochastic spatial Lotka-Volterra (LV) model for predator-prey interaction subject to a periodically varying carrying capacity. The LV model with on-site lattice occupation restrictions that represent finite food resources for…
In this paper we establish the orbital stability of periodic traveling waves for a general class of dispersive equations. We use the Implicit Function Theorem to guarantee the existence of smooth solutions depending of the corresponding…
We have studied properties of nonlinear waves in a mathematical model of a predator-prey system with pursuit and evasion. We demonstrate a new type of propagating wave in this system. The mechanism of propagation of these waves essentially…
In this paper we investigate a free boundary problem for the diffusive Leslie-Gower prey-predator model with double free boundaries in one space dimension. This system models the expanding of an invasive or new predator species in which the…
Different explanations have been proposed for the existence of colonial breeding behavior in birds, but field studies offer no conclusive results. We analyze the interplay between learning habits and predation pressure by means of numerical…