State Feedback Impulsive Model: Applications in Biomathematics and Engineering

During the development of biological mathematics, the ODE model significantly increased the effectiveness of solving problems of population size, sustainable survival, and infectious disease dynamics. Although the ODE model is quite suitable for describing the continuous, steady change of variables over time, some situations will show consistent transformations, then the variables will quickly and suddenly, exponentially alter without warning. For example, some animals give birth to offspring only a few days out of the year. Therefore, it is futile to express the population variation with a continuous ODE model. In a situation that stimulates a sudden change, we need a model which will describe both consistent transformations and sudden alterations. Fortunately, the state feedback impulsive model performs both tasks. In order to introduce some basic theorems about the state feedback impulsive model and its applications in biomathematics and engineering, we present this book.