By employing the operator theory, the Lyapunov function on time scales and the famous Gronwall's inequality, this paper addresses some dynamic properties of almost periodic solutions for a class of two species co-existence delayed model on time scales with almost periodic coefficients and Ricker, as well as the Beverton-Holt type function. First, we establish the existence and uniqueness of the almost periodic solution with a positive infimum by transforming the initial model into an equivalent integral equation. Second, we investigate the global exponential stability and uniformly asymptotic stability of the positive almost periodic solution. Finally, we give two examples to illustrate the main presented results.

This paper mainly considers the existence of the compact almost automorphic mild solution for a class of stochastic nonlinear differential equations. More specifically, based on $C_0$-semigroup theory, Hölder inequality, Burkholder–Davis–Gundy inequality and Lebesgue dominated convergence theorem, we obtain that the $K$-mild solution is uniformly continuous and is relatively compact, etc. Combined with the subvariant functional method, we give some sufficient conditions to make sure that there exists at least one minimal $K$-mild solution; further, if the minimal $K$-mild solution is unique, then it is compact and almost automorphic. Moreover, we provide an example to illustrate the main presented results.