Oscillations and global attractivity in delay differential equations of population dynamics

Almost periodicity of impulsive Hematopoiesis model with infinite delay

“…Moreover, we investigate exponential stability of the almost periodic positive solution by means of Liapunov functional. The results of this paper complement the past results in [22,6,7,12,13,17,18,20].…”

“…Gyori and Ladas [6] investigated the global attractivity of positive equilibrium for this model. Moreover, the above Hematopoiesis model and some generalized models have been studied by many authors, see [22,7,12,13,17,18,20]. The assumption that the environment is constant is rarely the case in real life.…”

Notice of Retraction: Stability and bifurcation analysis in a Mackey-Glass system

“…At first, we have that the only root of (5) with 7 = ° is negative when "I > ( n � 2 ) {3 . From the analysis leading to relation (7) we know that, if "I > ( n � 2 ) {3, (5) has no purely imaginary root iw with w > 0. Since A = ° is not a root of (5), we know that, for any 7 ;;" 0, (5) has no roots on the imaginary axis.…”

“…From the analysis leading to relation (7) we know that, if "I > ( n � 2 ) {3, (5) has no purely imaginary root iw with w > 0. Since A = ° is not a root of (5), we know that, for any 7 ;;" 0, (5) has no roots on the imaginary axis. Applying a result of Ruan and Wei [9, corollary 2.4], we arrive at the conclusion (i).…”

“…Equation (1) and (2) have been extensively studied in the literature. A majority of results on then deal with the global attractive of the positive equilibrium and oscillatory behaviors of solutions (see [3][4][5]). Meanwhile, there are several papers on the complex dynamics to (2).…”