In this paper, we study dynamic commensalism model with nonmonotic functional response, density dependent birth rates on time scales and derive sufficient conditions for the permanence. We also establish the existence and uniform asymptotic stability of unique almost periodic positive solution of the model by using Lyapunov functional method.

This paper is concerned with the dynamical stability analysis for almost periodic solution of memristive neural networks with time-varying delays. Under the framework of Filippov solutions, by applying the inequality analysis techniques, the existence and asymptotically almost periodic behavior of solutions are discussed. Based on the differential inclusions theory and Lyapunov functional appro...

The discrete analog of the well-known Favard Theorem states that the linear difference equation (1) x(t + 1) = A(t)x(t) + f(t) (t ∈ Z) with Bohr almost periodic coefficients admits at least one Bohr almost periodic solution if it has a bounded solution. The main assumption in this theorem is the separation among bounded solutions of the homogeneous equations (2) x(t + 1) = B(t)x(t), where B ∈ H...

We first propose the concept of almost periodic time scales and then give the definition of almost periodic functions on almost periodic time scales, then by using the theory of calculus on time scales and some mathematical methods, some basic results about almost periodic differential equations on almost periodic time scales are established. Based on these results, a class of highorder Hopfiel...