In this paper, we formulate an SEIRS epidemic model with two time delays and pulse vaccination. By estabishing stroboscopic map, we obtain the exact infection free periodic solution of the impulsive epidemic system. According to the comparison arguments, we obtain the sufficient conditions of global attractivity of the infection free periodic solution. Moreover, our results show that a large va...

Recently, there has been a lot of interest in studying the global attractivity, the boundedness character, and the periodicity nature of nonlinear difference equations see for example, [1– 22]. The study of the nonlinear rational difference equations of a higher order is quite challenging and rewarding, and the results about these equations offer prototypes towards the development of the basic ...

By constructing suitable Liapunov functionals and estimating uniform upper and lower bounds of solutions, sufficient conditions are obtained for the global attractivity of positive periodic solutions of the delay differential system with feedback control dy/dt = y(t)F(t, y(t − τ1(t)), . . . , y(t − τn(t)),u(t − δ(t))), du/dt = −η(t)u(t) + a(t)y(t − σ(t)). When these results are applied to the p...

This paper formulates a robust stage-structured SI eco-epidemiological model with periodic constant pulse releasing of infectious pests with pathogens. The authors show that the conditions for global attractivity of the ‘pest-eradication’ periodic solution and permanence of the system depend on time delay, hence, the authors call it “profitless”. Further, the authors present a pest management s...

In this paper, an SI epidemic model with stage structure is investigated. In this model, impulsive biological control which release infected pest to the field at a fixed time periodically is considered, and obtained the sufficient conditions for the global attractivity of pest-extinction periodic solution and permanence of the system. We also prove that all solutions of the model are uniformly ...

We study some aspects of the global dynamics of an n-dimensional Lotka-Volterra system with infinite delay and patch structure, such as extinction, persistence, existence and global attractivity of a positive equilibrium. Both the cases of an irreducible and reducible linear community matrix are considered, and no restriction on the signs of the intraand inter-specific delayed terms is imposed....

In this paper, we consider a non-autonomous stochastic LotkaVolterra competitive system dxi(t) = xi(t)[(bi(t)− n ∑ j=1 aij(t)xj(t))dt+σi(t)dBi(t)], where Bi(t) (i = 1, 2, · · · , n) are independent standard Brownian motions. Some dynamical properties are discussed and the sufficient conditions for the existence of global positive solutions, stochastic permanence, extinction as well as global at...

* Correspondence: [email protected] Department of Basic Courses, Hebei Finance University, Baoding 071000, China Abstract This article is concerned with the following rational difference equation yn+1 = (yn + yn-1)/(p + ynyn-1) with the initial conditions; y-1, y0 are arbitrary positive real numbers, and p is positive constant. Locally asymptotical stability and global attractivity of the ...

The paper addresses problems of analysis and control of spatial behavior of uncertain dynamical systems associated with properties of invariance and attractivity of smooth geometric objects (goal sets). The use of geometric control theory and inequalities of passivity allows one to reduce the problems to input-to-state stability with respect to part of the variables, construct Lyapunov-like sto...

The main goal of the paper is to investigate boundedness, invariant intervals, semicycles, and global attractivity of all nonnegative solutions of the equation xn 1 α βxn γxn−k / 1 xn−k , n ∈ N0, where the parameters α, β, γ ∈ 0,∞ , k ≥ 2 is an integer, and the initial conditions x−k, . . . , x0 ∈ 0,∞ . It is shown that the unique positive equilibrium of the equation is globally asymptotically ...