A new approach to the existence, nonexistence and uniqueness of positive almost periodic solution for a model of Hematopoiesis

Existence and Exponential Stability of Positive Almost Periodic Solutions for a Model of Hematopoiesis

“…Its study was initiated by Bohr in 24 . To the best of the authors' knowledge, there are a few published papers considering the notion of almost periodicity of delay differential equations with or without impulses, see [25][26][27][28][29][30][31][32][33][34][35][36] . Motivated by this, the aim of this paper is to establish sufficient conditions for the existence and exponential stability of positive almost periodic solution of nonlinear impulsive delay model of hematopoiesis of form 1.2 .…”

Positive almost periodic solution for a class of Nicholson’s blowflies model with multiple time-varying delays

“…On the other hand, in the real world, the delays in differential equations of population and ecology problems are usually time-varying. Moreover, it is known that the existence and stability of positive almost periodic solutions play a key role in characterizing the behavior of a dynamical system (see [14][15][16][17]). Thus, it is worthwhile continuing to investigate the existence and convergence of positive almost periodic solutions of Nicholson's blowflies model with time-varying delays.…”

Global exponential stability of periodic solutions in a nonsmooth model of hematopoiesis with time‐varying delays

“…In recent years, many remarkable works (e.g., [3,4,[11][12][13][14][15][16][17] and the references therein) concerning the dynamics of periodic solutions have been investigated. To the best of knowledge, however, this is the first attempt to deal with the periodic dynamics of model (1.2), which implies that the main results obtained in this paper are essentially new and complement complement previously known results.…”

“…In this model, x.t/ denotes the density of mature cells in blood circulation, a is the lost rate of the cells from the circulation, the flux b 1Cx n .t / of the cells into the circulation from the stem cell compartment depends on the number of cells x.t / at time t , b is the maximal production rate, and is the time delay between the production of immature cells in the bone marrow and their maturation for release in circulating bloodstream. As a classical model of population dynamics, model (1.1) and its modifications have received great attention from both theoretical and mathematical biologists and have long been considered as an active research area in recent years (e.g., [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and the references therein).…”