Global asymptotic stability of a discrete periodic haematopoietic model with mixed feedbacks

This paper is devoted to study a discrete haematopoietic model that is driven by mixed feedback control mechanisms. Based on the human body's demand for cells, the increase and decrease of blood cell number are regulated with the synergistic feedbacks of monotonically decreasing production function and unimodal production function in this model. We first deal with the sufficient condition for the existence of the positive periodic solution. This sufficient condition can be easily checked by the ratio of the variable coefficient of the extinction part to the variable coefficient of the production part. Moreover, we investigate the global asymptotic stability of a unique positive periodic solution. To this end, the upper and lower limits of all the positive solutions and the characteristics of mixed production functions are discussed to carry out the detailed analysis. Finally, with the clinical blood cell level, a concrete example is presented to verify our theoretical results.