Global Attractivity for Lasota–Wazewska-Type System with Patch Structure and Multiple Time-Varying Delays

Abstract

This paper aims to study the asymptotic behavior of Lasota–Wazewska-type system with patch structure and multiple time-varying delays. Based on the fluctuation lemma and some differential inequality techniques, we prove that the positive equilibrium is a global attractor of the addressed system with small time delay. Finally, we provide an example to illustrate the feasibility of the theoretical results.

Bistable and oscillatory dynamics of Nicholson's blowflies equation with Allee effect

“…When k = 1, it becomes the classical Nicholson's blowflies equation which has been extensively studied in the literature [2,6,28,30,32,38,42] and references cited therein. For the multiple-patch Nicholson's blowflies model, corresponding results can be found in [10,11,17,18,27,40,41] and references cited therein. When k ̸ = 1, equation ( 2) appears as a model for the process of generation and degeneration of red blood cells [14,37].…”

Delay-dependent attractivity on a tick population dynamics model incorporating two distinctive time-varying delays

“…In the second place, large delays may lead to complex dynamic behaviour. It is worth noting that assumption (1.3) mentioned in the Introduction is not satisfied for (4.1), and the global attractivity on the positive equilibrium point for the tick population dynamics model involving two distinctive delays has not been touched in [1,2,[10][11][12][13][14][15][16][17][18][19][20][21][22][23][27][28][29][30][31][32][33]. One can see that all the conclusions in the above mentioned references cannot be utilized to reveal the global attractivity of (4.1).…”

Global dynamics of neoclassical growth model with multiple pairs of variable delays

“…We should point out that the asymptotic behavior of differential neoclassical growth model with multiple pair of variable delays has not yet been touched, and the related literatures on this challenge issue appear to be scarce. One can see that the above mentioned references [5,8,10,11,13,[15][16][17][18][19][20][21][29][30][31][32][33][34][35][36]] cannot be employed to example 4.1.…”

“…Nowadays, more and more scientists have recognized that delays inevitably occur in economic activities and may be an essential source of macroeconomic dynamics [5,6]. When γ = 0, equation (1.1) is called as Lasota-Wazewska-type delay differential equation, which is applied to describe the survival of red blood cells in an animal [7,8]. If γ = 1, system (1.1) turns to be well-known Nicholson's blowflies population model, which has been intensively investigated to model the oscillatory fluctuations of the laboratory population of the Australian sheep blowfly Lucilia cuprina [9][10][11][12][13][14][15].…”