Related papers: Periodic solutions for a delayed competitive chemo…
We consider a two-component competition-diffusion system with equal diffusion coefficients and inhomogeneous Dirichlet boundary conditions. When the interspecific competition parameter tends to infinity, the system solution converges to…
Microbial communities routinely have several alternative stable states observed for the same environmental parameters. Sudden and irreversible transitions between these states make external manipulation of these systems more complicated. To…
We study linear inhomogeneous kinetic equations with an external confining potential and a collision operator admitting several local conservation laws (local density, momentum and energy). We classify all special macroscopic modes…
We show the continuous dependence of solutions of linear nonautonomous second order parabolic partial differential equations (PDEs) with bounded delay on coefficients and delay. The assumptions are very weak: only convergence in the weak-*…
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…
How do decisions change with the economic environment and with time? This paper studies general nonstationary stopping problems and provides the methodological tools to answer these questions. First, we identify conditions that ensure a…
We consider a discrete time competition model. Populations compete for common limited resources but they have different fertilities and mortalities rates. We compare dynamical properties of this model with its continuous counterpart. We…
This study presents a mathematical model that describes the relationship between the Puma concolor and its prey using delay differential equations, a Holling type III functional response, logistic growth for the prey, and a Ricker-type…
In this work the existence of periodic solutions is studied for the Hamiltonian functions (Formula presented.) where the first term consist of a harmonic oscillator and the second term are homogeneous polynomials of degree 5 defined by two…
A class of variational models describing ecological systems of k species competing for the same resources is investigated. The occurrence of coexistence in minimal energy solutions is discussed and positive results are proven for suitably…
We study the dynamics of a piecewise-linear second-order delay differential equation that is representative of feedback systems with relays (switches) that actuate after a fixed delay. The system under study exhibits strong…
In this paper, we consider a multi-layer tumor model with a periodic provision of external nutrients. The domain occupied by tumor has a different shape (flat shape) than spherical shape which has been studied widely. The important…
We consider a two-species chemotaxis model in $\R^d(d \ge 3)$ featuring nonlinear porous medium-type diffusion and nonlocal attractive power-law interaction. Here, the nonlinear diffusion is chosen to be $1/m_1+1/m_2=(d+2)/d$ in such a way…
In this paper, we study the time periodic problem to a three-dimensional chemotaxis-Stokes model with porous medium diffusion $\Delta n^m$ and inhomogeneous mixed boundary conditions. By using a double-level approximation method and some…
An impulsive model of augmentative biological control consisting of a general continuous predator-prey model in ordinary differential equations augmented by a discrete part describing periodic introductions of predators is considered. It is…
In this paper, we consider periodic predator-prey systems of Leslie-Gower or Holling-Tanner type, assuming that the coefficients are continuous positive $\omega$-periodic functions. We prove an existence of positive $\omega$-periodic…
A modified method of functional constraints is used to construct the exact solutions of nonlinear equations of reaction-diffusion type with delay and which are associated with variable coefficients. This study considers a most generalized…
The periodic solutions of a type of nonlinear hyperbolic partial differential equations with a localized nonlinearity are investigated. For instance, these equations are known to describe several acoustical systems with fluid-structure…
The main purpose of this paper is to provide a summary of the fundamental methods for analyzing delay differential equations arising in biology and medicine. These methods are employed to illustrate the effects of time delay on the behavior…
This is the first of two papers where we discuss the limits imposed by competition to the biodiversity of species communities. In this first paper we study the coexistence of competing species at the fixed point of population dynamic…