Extinction and permanence of two-nutrient and one-microorganism chemostat model with pulsed input

Global Behaviors of a Chemostat Model with Delayed Nutrient Recycling and Periodically Pulsed Input

The dynamic behaviors in a chemostat model with delayed nutrient recycling and periodically pulsed input are studied. By introducing new analysis technique, the sufficient and necessary conditions on the permanence and extinction of the microorganisms are obtained. Furthermore, by using the Liapunov function method, the sufficient condition on the global attractivity of the model is established...

Species extinction and permanence of an impulsively controlled two-prey one-predator system with seasonal effects

Recently, the population dynamic systems with impulsive controls have been researched by many authors. However, most of them are reluctant to study the seasonal effects on prey. Thus, in this paper, an impulsively controlled two-prey one-predator system with the Beddington-DeAngelis type functional response and seasonal effects is investigated. By using the Floquet theory, the sufficient condit...

Dynamic Behaviors in a Droop Model for Phytoplankton Growth in a Chemostat with Nutrient Periodically Pulsed Input

Research Article On the Study of Chemostat Model with Pulsed Input in a Polluted Environment

a comparison of teachers and supervisors, with respect to teacher efficacy and reflection

supervisors play an undeniable role in training teachers, before starting their professional experience by preparing them, at the initial years of their teaching by checking their work within the proper framework, and later on during their teaching by assessing their progress. but surprisingly, exploring their attributes, professional demands, and qualifications has remained a neglected theme i...