Almost periodic solutions of delay difference systems

Global attractivity and almost periodic solution of a discrete mutualism model with delays

“…By Theorem 3.4 in , we can easily obtain the lemma as follows. Lemma If each hull equation of system has a unique strictly positive solution, then the almost periodic difference system has a unique strictly positive almost periodic solution. Theorem If the almost periodic difference system satisfies , then the almost periodic difference system admits a unique strictly positive almost periodic solution, which is globally attractive. Proof By Lemma , we only need to prove that each hull equation of system has a unique globally attractive almost periodic sequence solution; hence, we first prove that each hull equation of system has at least one strictly positive solution (the existence), and then we prove that each hull equation of system has a unique strictly positive solution (the uniqueness).…”

“…By the almost periodic theory, we can conclude that if system (1.2) satisfies (4.6), then the hull equation (5.1) of system (1.2) also satisfies (4.6). By Theorem 3.4 in [18], we can easily obtain the lemma as follows.…”

“…By the biological meaning, we will focus our discussion on the positive solutions of system . So, it is assumed that the initial conditions of system are the form With the stimulation from the works , the main purpose of this paper is to obtain a set of sufficient conditions to ensure the existence of a unique globally attractive positive almost periodic solution of system with initial condition .…”

Existence of Unique and Global Asymptotically Stable Almost Periodic Solution of a Discrete Predator-Prey System with Beddington-DeAngelis Functional Response and Density Dependent

“…Definition 2.1. ( [28]). A sequence z : Z −→ R is called an almost periodic sequence if the ε−translation set of z, E{ε, z} = {τ ∈ Z :…”

Permanence and almost periodic sequence solution for a discrete delay logistic equation with feedback control

“…Recently, many scholars have paid attention to the non-autonomous discrete population models, since the discrete time models governed by difference equation are more appropriate than the continuous ones when the populations have nonoverlapping generations (see [4][5][6][7][8][9][10]). Moreover, since the discrete time models can also provide efficient computational models of continuous models for numerical simulations, it is reasonable to study discrete time models governed by difference equations.…”