Nicholson’s blowflies differential equations revisited: Main results and open problems

Periodic solutions in general scalar non-autonomous models with delays

“…In the literature, we found (in historical order) the studies for general non-autonomous models [7,10,[14][15][16]18,[22][23][24]28,31,[34][35][36][37][39][40][41][42][43] with some applications for the particular models. The results obtained separately for some classical models described in the Appendix were presented in [1][2][3][4][5][6]8,9,11,13,17,[19][20][21]26,37,38]. We begin with the most celebrated class of semilinear models:…”

“…Consider the following Nicholson's blowflies model with a nonlinear density-dependent mortality term, introduced in [3]:…”

Existence and Global Exponential Stability of Positive Almost Periodic Solutions for a Delayed Nicholson's Blowflies Model

“…More details on biological explanation to model (1.1) can be found in [1] and [28]. Subsequently, there have been extensive results in the literature on the most important qualitative properties of the model and its analogous equations such as existence of positive solutions, persistence, permanence, oscillation and stability; some of the results can be found in [2,4,11,14,17,29].…”

“…We refer the reader to [5,12,13,18,21,20,24,32] and the references cited therein. Recently, as pointed out by L. Berezansky et al [1], a new study indicates that a linear model of density-dependent mortality will be most accurate for populations at low densities, and marine ecologists are currently in the process of constructing new fishery models with nonlinear density-dependent mortality rates. Therefore, L. Berezansky et al [1] and W. Wang [28] proposed the following Nicholson's blowflies model with a nonlinear density-dependent mortality term:…”

Global Exponential Stability of Periodic Solutions for a Nicholson’s Blowflies Model with a Linear Harvesting Term

“…Later, the theory of Nicholson's blowflies equation has been made a remarkable progress in the past many years. Recently, L. Berezansky et al [3] had made a review about the Nicholsons blowflies differential equations, and presented the following model proposed the following Nicholson's blowflies model:…”