A nonautonomous discrete two-species Lotka-Volterra commensalism system with delays is considered in this paper. Based on the discrete comparison theorem, the permanence of the system is obtained. Then, by constructing a new discrete Lyapunov functional, a set of sufficient conditions which guarantee the system global attractivity are obtained. If the coefficients are almost periodic, there exists an almost periodic solution and the almost periodic solution is globally attractive.

A two species non-autonomous competitive phytoplankton system with nonlinear inter-inhibition terms and one toxin producing phytoplankton is studied in this paper. Sufficient conditions which guarantee the extinction of a species and the global attractivity of the other one are obtained. Some parallel results corresponding to Yue (Adv. Differ. Equ. 2016Equ. :1, 2016Equ. , doi:10.1007 are established. Numeric simulations are carried out to show the feasibility of our results.

The stability of a kind of cooperative model incorporating harvesting is revisited in this paper. By using an iterative method, the global attractivity of the interior equilibrium point of the system is investigated. We show that the condition which ensures the existence of a unique positive equilibrium is enough to ensure the global attractivity of the positive equilibrium. Our results significantly improve the corresponding results of Wei and Li (2013).

A nonautonomous modified Leslie-Gower predator-prey model with Holling-type II schemes and a prey refuge is studied in this paper. Persistent property and stability property of the system are investigated. Some findings about the influence of prey refuge are obtained.

Sufficient conditions are obtained for the global attractivity of the following integrodifferential model of mutualism:dN1(t)/dt=r1N1(t)[((K1+α1∫0∞J2(s)N2(t-s)ds)‍/(1+∫0∞J2(s)N2(t-s)ds))‍-N1(t)],dN2(t)/dt=r2N2(t)[((K2+α2∫0∞J1(s)N1(t-s)ds)‍/(1+∫0∞J1(s)N1(t-s)ds‍))-N2(t)], whereri,Ki,andαi,i=1,2, are all positive constants. Considerαi>Ki,i=1,2.Consider  Ji∈C([0,+∞),[0,+∞))and∫0∞‍Ji(s)ds=1,i=1,2.Our result shows that conditions which ensure the permanence of the system are enough to ensure the global stability of the system. The result not only improves but also complements some existing ones.