Dynamics of Nicholson’s blowflies models with a nonlinear density-dependent mortality

Novel stability criteria on nonlinear density-dependent mortality Nicholson’s blowflies systems in asymptotically almost periodic environments

“…The collection of the asymptotically almost-periodic functions will be labeled by AAP(R, J). For more details on the above definitions, we refer the readers to [8,9,11,12]. It will be supposed that…”

“…In particular, the results in [1-6, 8, 9, 15-46] give no conclusion about the problem of asymptotically almost-periodic dynamics of Nicholson's blowflies models involving such a patch structure. Hence, all results in [1][2][3][4][5][6][7][8][9][10] and cannot be straightforwardly employed to validate that all solutions of (4.1) converge globally to the almost-periodic function.…”

“…Because the almost-periodic oscillation is an important dynamic characteristic in population dynamics, more attention has been paid to the almost-periodic problems for delayed Nicholson's blowflies equation and and its variants [7][8][9]. Furthermore, a recent study in [10] established the existence and global stability of almost-periodic solutions for Nicholson's blowflies system (1.1) involving a positive constant M > κ obeying γ ij (t)M ≤ κ, for all t ∈ R, i ∈ Q, j ∈ I = {1, 2, .…”

“…(1.6) Alas, the additional assumptions (1.2)-(1.5) are all defined on R, which are evidently not in accord with the biological interpretation in the considered systems. Apparently, according to the biological background of (1.2) in [8,9], one needs to relax the above additional assumptions as follows:…”

Stepanov-Like Asymptotical Almost Periodic Functions and an Application

“…Since then, asymptotically almost periodic functions have become a very important function class and to find asymptotically almost periodic solutions for differential equations has been a hot topic for researchers. For the basic properties of asymptotical almost periodic functions, we refer the reader to [19] and for some recent papers about the existence of asymptotically almost periodic solutions for differential equations arising in theory and application, we refer the reader to [20][21][22][23][24][25]. However, up to now, few studies have been done on Stepanov-like asymptotical almost periodic functions [26], but these studies are necessary.…”