Dynamics Of Two Bacterial Species Model With Discontinuous Antibiotics Input

With the development of antibiotic studying, people have paid more and more attention to antibiotic abuse. Many scholars studied the impact of antibiotic on bacterial species through the establishment of mathematical models, and got a lot of conclusions of clinical guiding significance. The discussions of continuous biological dynamical systems were main research direction in the past decades. Recently, people also find that continuous biological dynamical systems can not represent some natural phenomena and human activities accurately. Impulsive dynamical systems then turn out to be the hotspot of mathematical biology since the relatively instantaneous behavior can be described well in impulsive differential equations. Impulsive dynamic system is possible one of the most youthy and most attracting fields in main mathematical branches such as differential equation, dynamical systems and control theories. The theory of impulsive differential equations is not only richer than corresponding theory of differential equations but also represents a more natural framework for mathematical model of many real world phenomena. In this thesis, based on impulsive differential equations, we investigate the dynamics of two bacterial species model with discontinuous impulsive antibiotics input. We give some threshold conditions which can keep the populations persistent survival or extinction.In chapter 1, we introduce the definition of impulsive differential equation and related knowledge. In chapter 2, we propose a two bacterial species model with discontinuous impulsive antibiotics input and study the dynamics of such system. We get the conditions of persistence and extinction about the system. In chapter 3, we discuss the dynamics of two bacteria species model with discontinuous antibiotics input and time delay, we obtain conditions for globally attractive and persistence of bacteria species. We show that discontinuous antibiotics input can bring great effects on the dynamics of the system, and antibiotics time delay is harmless. Moreover, in the end of each chapter, we give some numeric simulation results which confirm the theoretical conclusions.