Permanence and exponential stability for generalised nonautonomous Nicholson systems

The paper is concerned with nonautonomous generalised Nicholson systems under conditions which imply their permanence: by refining the assumptions for permanence, explicit lower and upper uniform bounds for all positive solutions are provided, as well as criteria for the global exponential stability of these systems. In particular, for periodic systems, conditions for the existence of a globally exponentially attractive positive periodic solution are derived

Permanence for a class of non-autonomous delay differential systems

We are concerned with a class of n-dimensional non-autonomous delay differential equations obtained by adding a non-monotone delayed perturbation to a linear homogeneous cooperative system of delay differential equations. Sufficient conditions for the exponential asymptotic stability of the linear system are established. By using this stability, the permanence of the perturbed nonlinear system is studied. Under more restrictive constraints on the coefficients, the system has a cooperative type behaviour, in which case explicit uniform lower and upper bounds for the solutions are obtained. As an illustration, the asymptotic behaviour of a non-autonomous Nicholson system with distributed delays is analysed

Permanence for a class of non-autonomous delay differential systems

We are concerned with a class of n-dimensional non-autonomous delay differential equations obtained by adding a non-monotone delayed perturbation to a linear homogeneous cooperative system of delay differential equations. Sufficient conditions for the exponential asymptotic stability of the linear system are established. By using this stability, the permanence of the perturbed nonlinear system is studied. Under more restrictive constraints on the coefficients, the system has a cooperative type behaviour, in which case explicit uniform lower and upper bounds for the solutions are obtained. As an illustration, the asymptotic behaviour of a non-autonomous Nicholson system with distributed delays is analysed

Permanence and exponential stability for generalised nonautonomous Nicholson systems

The paper is concerned with nonautonomous generalised Nicholson systems under conditions which imply their permanence: by refining the assumptions for permanence, explicit lower and upper uniform bounds for all positive solutions are provided, as well as criteria for the global exponential stability of these systems. In particular, for periodic systems, conditions for the existence of a globally exponentially attractive positive periodic solution are derived

Persistence of nonautonomous logistic system with time-varying delays and impulsive perturbations

In this paper, we develop the impulsive control theory to nonautonomous logistic system with time-varying delays. Some sufficient conditions ensuring the persistence of nonautonomous logistic system with time-varying delays and impulsive perturbations are derived. It is shown that the persistence of the considered system is heavily dependent on the impulsive perturbations. The proposed method of this paper is completely new. Two examples and the simulations are given to illustrate the proposed method and results