Applied impulsive mathematical models
As a continuation of the book [the first author, Stability analysis of impulsive functional differential equations. Berlin: Walter de Gruyter (2009; Zbl 1189.34001)], this book under review presents a description of some recent developments in the study of mathematical models in the form of impulsive differential equations, which are mainly impulsive ordinary differential equations. The material in this book is divided into six chapters. Chapter 1 is a brief introduction. Chapter 2 introduces the basic theory for the qualitative investigations of impulsive mathematical models, such as the basic definitions and properties of almost periodic sequences and almost periodic piecewise continuous functions, the stability and boundedness of solutions of some impulsive models, and some classes of piecewise continuous Lyapunov functions and Lyapunov functionals. In Chapter 3, qualitative properties of the solutions are investigated for an impulsive Lasota-Wazewska model, an impulsive model of hematopoiesis and an impulsive delay logarithmic population model. The stability of the zero solution of an \(n\)-dimensional impulsive biological model is also investigated in the chapter by using vector Lyapunov functions and the comparison principle. Chapter 4 states some existence theorems for almost periodic solutions and some stability and boundedness results for some classes of impulsive Lotka-Volterra models without or with finite or infinite delays, and some uniform stability and uniform asymptotic stability results for a class of impulsive Kolmogorov-type delayed systems of nonautonomous differential equations. Chapter 5 contains some sufficient conditions for the existence of almost periodic solutions, global asymptotic stability, and global exponential stability of some impulsive neural network models with delays including impulsive Hopfield neural network models and Bidirectional Associative Memory (BAM) neural network models. The last chapter concerns the stability of impulsive delayed Solow-type models and the uniform asymptotic stability and almost periodicity of impulsive price fluctuations models. I think it is an interesting book, and I recommend it to the students and researchers interested in impulsive models.
scientific article; zbMATH DE number 6538774