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A nonlinear cyclic system with delay and the overall negative feedback is considered. The characteristic equation of the linearized system is studied in detail. Sufficient conditions for the oscillation of all solutions and for the…
A general system of difference equations is presented for multispecies communities with density dependent population growth and delayed maturity. Interspecific competition, mutualism, predation, commensalism, and amensalism are…
A nonlinear stochastic differential equation with the order of nonlinearity higher than one, with several discrete and distributed delays and time varying coefficients is considered. It is shown that the sufficient conditions for…
Self-regulatory models are common in nature, as described e.g. in (\cite{mur}), (\cite{ha}) and (\cite{Gb}).\\ Let us consider a system made up of a number of glands as a motivation. Each gland secretes a hormone that allows secretion in…
This paper is devoted to a nonlocal dispersal logistic model with seasonal succession in one-dimensional bounded habitat, where the seasonal succession accounts for the effect of two different seasons. Firstly, we provide the…
In this paper, we consider the almost periodic dynamics of an impulsive multispecies Lotka-Volterra competition system with time delays on time scales. By establishing some comparison theorems of dynamic equations with impulses and delays…
Some systems of parabolic equations with nonlocal initial conditions are studied. The systems arise when considering steady-state solutions to diffusive age-structured cooperative or competing species. Local and global bifurcation…
A chemostat enables long-term, continuous, exponential-phase growth in an environment limited as prescribed by the researcher. It is thus a potent tool for laboratory evolution - selecting for strains with desired phenotypes. However,…
In this paper, we give a sufficient condition for the existence, nonexistence and uniqueness of coexistence of positive solutions to a rather general type of elliptic competition system.
We consider $N$-species nonautonomous competitive systems of partial differential equations of Kolmogorov type. Under the Neumann boundary conditions we give a sufficient condition for the system to be uniformly stable and globally…
We investigate some chemostat models incorporating wall growth, competition, random fluctuations on the dilution rate, and different consumption functions (Monod and Haldane). We analyze the asymptotic behavior of the solutions of the…
This article is dedicated to the study and comparison of two chemostat-like competition models in a heterogeneous environment. The first model is a probabilistic model where we build a PDMP simulating the effect of the temporal…
One of the classical models in mathematical biology is the Lotka-Volterra competition model, describing the dynamics of two populations competing for resources. Two possible regimes in this system are given by their coexistence or…
A novel method is developed for constructing periodic solutions of a model equation describing nonlocal Josephson electrodynamics. This method consists of reducing the equation to a system of linear ordinary differential equations through a…
The oscillatory behavior of the solutions to a differential equation with several non-monotone delay arguments and non-negative coefficients is studied. A new sufficient oscillation condition, involving lim sup, is obtained. An example…
In this work we provide conditions for the existence of periodic solutions to nonlinear, second-order difference equations of the form \begin{equation*} y(t+2)+by(t+1)+cy(t)=g(t,y(t)) \end{equation*} where $c\neq 0$, and…
We provide explicit conditions for uniform stability, global asymptotic stability and uniform exponential stability for dynamic equations with a single delay and a nonnegative coefficient. Some examples on nonstandard time scales are also…
This paper examines impulsive non-autonomous systems with grazing periodic solutions. Surfaces of discontinuity and impact functions of the systems are not depending on the time variable. That is, we can say that the impact conditions are…
We propose a system of differential equations modeling the competition between two obligate mutualistic species for a single nutrient in a chemostat. Each species promotes the growth of the other, and growth occurs only in the presence of…
We propose a novel method for fast and scalable evaluation of periodic solutions of systems of ordinary differential equations for a given set of parameter values and initial conditions. The equations governing the system dynamics are…