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

Abstract

Taking into account the effects of multiple pairs of variable delays, this paper deals with the global dynamics for a class of differential neoclassical growth models. We aim to obtain significant insights into better understanding of how the multiple pairs of variable delays essentially affect the stability and attractiveness of the unique positive equilibrium point. First of all, we prove that every solution of the IVP (initial value problem) with respect to the addressed system exists globally and is positive and bounded above. Secondly, with the help of the methods of fluctuation lemma and analytical techniques, two delay-independent criteria and one delay-dependent criterion on the attractivity of the unique positive equilibrium point are established, which improve and complement some published results. Lastly, two examples with the numerical simulation are arranged to illustrate the effectiveness and feasibility of the obtained 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].…”

“…Theorem 3.4. Assume that β * < β < β, τ > 0 and the initial function ϕ satisfies (10). Let u(t) be the solution of (3).…”

Global population dynamics of a single species structured with distinctive time-varying maturation and self-limitation delays

“…As [6,21,14], in [16,11], the authors still were unable to derive any global convergence for the positive equilibrium point of (1.2). Theorem 3.1 complements the aforementioned works and this seems to be the first time that such a result is derived for this type of Nichlson's blowflies equation.…”

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).…”