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Using the theory of impulsive differential equations, this book focuses on mathematical models which reflect current research in biology, population dynamics, neural networks and economics. The authors provide the basic background from the fundamental theory and give a systematic exposition of recent results related to the qualitative analysis of impulsive mathematical models. Consisting of six chapters, the book presents many applicable techniques, making them available in a single source easily accessible to researchers interested in mathematical models and their applications. Serving as a valuable reference, this text is addressed to a wide audience of professionals, including mathematicians, applied researchers and practitioners.

Mathematics. --- Economics, Mathematical. --- System theory. --- Statistical physics. --- Systems Theory, Control. --- Nonlinear Dynamics. --- Mathematical Biology in General. --- Quantitative Finance. --- Mathematics --- Mathematical models. --- Study and teaching. --- Models, Mathematical --- Simulation methods --- Systems theory. --- Finance. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Mathematical and Computational Biology. --- Funding --- Funds --- Economics --- Currency question --- Biomathematics. --- Economics, Mathematical . --- Mathematical economics --- Econometrics --- Biology --- Physics --- Mathematical statistics --- Systems, Theory of --- Systems science --- Science --- Methodology --- Statistical methods --- Philosophy

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In recent years, there has been a tremendous amount of research activity in the general area of population dynamics, particularly the Lotka-Volterra system, which has been a rich source of mathematical ideas from both theoretical and application points of view. In spite of the technological advances, many authors seem to be unaware of the bulk of the work that has been done in this area recently. This often leads to duplication of work and frustration to the authors as well as to the editors of various journals. This book is built out of lecture notes and consists of three chapters written by four mathematicians with overlapping expertise that cover a broad sector of the research in this area. Each chapter consists of carefully written introductory exposition, main breakthroughs, open questions and bibliographies. The chapters present recent developments on topics involving the dynamic behavior of solutions and topics such as stability theory, permanence, persistence, extinction, existence of positive solutions for the Lotka-Volterra and related systems. This fills a void in the literature, by making available a source book of relevant information on the theory, methods and applications of an important area of research.

Lotka-Volterra equations. --- Population biology --- Predator-prey equations --- Biology --- Differential equations, Nonlinear --- Mathematical models. --- Mathematical models --- Lotka-Volterra System. --- Population Dynamics.