Oscillation of θ-methods for the Lasota-Wazewska model

The aim of this paper is to discuss the oscillation of numerical solutions for the Lasota-Wazewska model. Using two θ-methods (the linear θ-method and the one-leg θ-method), some conditions under which the numerical solutions oscillate are obtained for different range of θ. Furthermore, it is shown that every non-oscillatory numerical solution tends to the fixed point of the original continuous equation. Numerical examples are given

Global asymptotic stability of pseudo almost periodic solutions to a Lasota–Wazewska model with distributed delays

In this paper, we study a class of Lasota-Wazewska model with distributed delays, new criteria for the existence and global asymptotic stability of positive pseudo almost periodic solutions are established by using the fixed point method and the properties of pseudo almost periodic functions, together with constructing suitable Lyapunov function. Finally, we present an example with simulations to support the theoretical results. The obtained results are essentially new and they extend previously known results

Almost automorphic delayed differential equations and Lasota-Wazewska model

Existence of almost automorphic solutions for abstract delayed differential equations is established. Using ergodicity, exponential dichotomy and Bi-almost automorphicity on the homogeneous part, sufficient conditions for the existence and uniqueness of almost automorphic solutions are given.Comment: 16 page

Positive Almost Periodic Solution for a Model of Hematopoiesis with Infinite Time Delays and a Nonlinear Harvesting Term

A generalized model of Hematopoiesis with infinite time delays and a nonlinear harvesting term is investigated. By utilizing a fixed point theorem of the differential equations and constructing a suitable Lyapunov functional, we establish some conditions which guarantee the existence of a unique positive almost periodic solution and the exponential convergence of the system. Finally, we give an example to illustrate the effectiveness of our results

Existence and global attractivity of positive periodic solutions for the impulsive delay Nicholson's blowflies model

AbstractIn this paper we shall consider the following nonlinear impulsive delay population model:(0.1)x′(t)=-δ(t)x(t)+p(t)x(t-mω)e-α(t)x(t-mω)a.e. t>0,t≠tk,x(tk+)=(1+bk)x(tk),k=1,2,…,where m is a positive integer, δ(t), α(t) and p(t) are positive periodic continuous functions with period ω>0. In the nondelay case (m=0), we show that (0.1) has a unique positive periodic solution x*(t) which is globally asymptotically stable. In the delay case, we present sufficient conditions for the global attractivity of x*(t). Our results imply that under the appropriate linear periodic impulsive perturbations, the impulsive delay equation (0.1) preserves the original periodic property of the nonimpulsive delay equation. In particular, our work extends and improves some known results

The existence of positive periodic solutions of a class of lotka-volterra type impulsive systems with infinitely distributed delay

AbstractIn this paper, the existence of positive periodic solutions of a class of periodic Lotka-Volterra type impulsive systems with distributed delays is studied. By using the continuation theorem of coincidence degree theory, a set of easily verifiable sufficient conditions are obtained, which improve and generalize some existing results

Almost periodic solutions for Fox production harvesting model with delay

By utilizing the continuation theorem of coincidence degree theory, we shall prove that a Fox production harvesting model with delay has at least one positive almost periodic solution. Some preliminary assertions are provided prior to proving our main theorem. We construct a numerical example along with graphical representations to illustrate feasibility of the theoretical result

Global attractivity of positive periodic solutions for an impulsive delay periodic model of respiratory dynamics

AbstractIn this paper we shall consider the following nonlinear impulsive delay differential equation x′(t)+αV(t)x(t)xn(t−mω)θn+xn(t−mω)=λ(t),a.e.t>0,t≠tk,x(tk+)=1(1+bk)x(tk),k=1,2,…,where m and n are positive integers, V(t) and λ(t) are positive periodic continuous functions with period ω>0. In the nondelay case (m=0), we show that the above equation has a unique positive periodic solution x∗(t) which is globally asymptotically stable. In the delay case, we present sufficient conditions for the global attractivity of x∗(t). Our results imply that under the appropriate periodic impulsive perturbations, the impulsive delay equation shown above preserves the original periodic property of the nonimpulsive delay equation. In particular, our work extends and improves some known results

Existence and global attractivity of periodic solution for impulsive stochastic Volterra-Levin equations

In this paper, we consider a class of impulsive stochastic Volterra-Levin equations. By establishing a new integral inequality, some sufficient conditions for the existence and global attractivity of periodic solution for impulsive stochastic Volterra-Levin equations are given. Our results imply that under the appropriate linear periodic impulsive perturbations, the impulsive stochastic Volterra-Levin equations preserve the original periodic property of the nonimpulsive stochastic Volterra-Levin equations. An example is provided to show the effectiveness of the theoretical results