This paper discusses a discrete multispecies Gilpin-Ayala mutualism system. We first study the permanence and global attractivity of the system. Assume that the coefficients in the system are almost periodic sequences, we obtain the sufficient conditions for the existence of a unique almost periodic solution which is globally attractive and uniformly asymptotically stable by constructing a suit...

The dynamic behaviors in a chemostat model with delayed nutrient recycling and periodically pulsed input are studied. By introducing new analysis technique, the sufficient and necessary conditions on the permanence and extinction of the microorganisms are obtained. Furthermore, by using the Liapunov function method, the sufficient condition on the global attractivity of the model is established...

In this paper, by using the contraction mapping principle and constructing a suitable Lyapunov functional, we established a set of easily applicable criteria for the existence, uniqueness and global attractivity of positive periodic solution and positive almost periodic solution of a neutral multi-species Logarithmic population model with multiple delays and impulses. The results improve and ge...

We investigate the local stability, prime period-two solutions, boundedness, invariant intervals, and global attractivity of all positive solutions of the following difference equation: yn 1 r pyn yn−k / qyn yn−k , n ∈ N0, where the parameters p, q, r ∈ 0,∞ , k ∈ {1, 2, 3, . . .} and the initial conditions y−k, . . . , y0 ∈ 0,∞ . We show that the unique positive equilibrium of this equation is ...

In this paper, we investigate the global attractivity of negative solutions of the nonlinear difference equation xn+1 = 1− xn−k A + xn , n = 0, 1, . . . , where A ∈ (−∞, 0), k is a positive integer and initial conditions x−k, · · · , x0 are arbitrary real numbers. We show that the unique negative equilibrium of abovementioned equation is a global attractor with a basin under certain conditions....

We prove a generalization of a measure theoretic fixed point theorem of Darbo in Banach spaces which includes some well-known fixed point theorems of Dhage and Sadovskii as special cases. A generalized nonlinear functional integral equation is studied via Dhage fixed point theorem for attractivity of the solutions on unbounded intervals of real line. Finally the validity of our hypotheses impos...