Dynamic behaviors of Monod type chemostat model with impulsive perturbation on the nutrient concentration

Analysis of a delayed Monod type chemostat model with impulsive input the polluted nutrient

“…Lemma 3.5 [33]. Considering the following impulsive system v 0 ðtÞ ¼ ÀDvðtÞÞ; t-ns; vðns þ Þ ¼ vðnsÞ þ Ts 0 ; t ¼ ns; n ¼ 1; 2; .…”

On the Uniform Stability of Impulsive Lotka-Volterra Type Systems with Supremums

“…In term of the mathematical treatment, the presence of pulses gives the system a mixed nature, both continuous and discrete [4,5,10,19]. For example, some impulsive differential equations have been recently introduced in population dynamics, such as vaccination [7], population growth models [2,3,14,16], chemotherapeutic treatment of disease [11], chemostat [20], pollution [13], the tumor-normal cell interaction [8], etc.…”

Study of chemostat model with impulsive input and nutrient recycling in a polluted environment

“…The chemostat models with impulsive input perturbation have been studied in [13][14][15][16][17]. Many important and interesting results on the _ SðtÞ ¼ ÀDSðtÞ À lSðtÞxðtÞ dðKþSðtÞÞ þ brxðtÞ; _ xðtÞ ¼ ÀDxðtÞ þ lSðtÞxðtÞ KþSðtÞ À rxðtÞ; t -nT Sðt þ Þ ¼ SðtÞ þ p;…”