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Dynamical Systems
This book offers a captivating exploration of the intersection between mathematics, chaos theory, and dynamical systems through the personal journeys of twelve renowned mathematicians and physicists from China, Europe, Russia, and the USA. The first section of the book provides an intimate look into the formative experiences and early steps of these scientists. In these life stories, the names of other famous mathematicians arise, crisscrossing all the stories in unexpected ways. The second part of the book explores the practical applications of chaotic attractors in various fields. These include chaos-based encryption in cryptography, sensor and actuator placement in Chua circuits for contr...
Difference Equations And Discrete Dynamical Systems - Proceedings Of The 9th International Conference
Difference Equations or Discrete Dynamical Systems is a diverse field which impacts almost every branch of pure and applied mathematics. Not surprisingly, the techniques that are developed vary just as broadly. No more so is this variety reflected than at the prestigious annual International Conference on Difference Equations and Applications. Organized under the auspices of the International Society of Difference Equations, the Conferences have an international attendance and a wide coverage of topics.The contributions from the conference collected in this volume invite the mathematical community to see a variety of problems and applications with one ingredient in common, the Discrete Dynamical System. Readers may also keep abreast of the many novel techniques and developments in the field.The special emphasis of the meeting was on mathematical biology and accordingly about half of the articles are in the related areas of mathematical ecology and mathematical medicine.
Difference and Differential Equations
This volume contains papers from the 7th International Conference on Difference Equations held at Hunan University (Changsa, China), a satellite conference of ICM2002 Beijing. The volume captures the spirit of the meeting and includes peer-reviewed survey papers, research papers, and open problems and conjectures. Articles cover stability, oscillation, chaos, symmetries, boundary value problems and bifurcations for discrete dynamical systems, difference-differential equations, and discretization of continuous systems. The book presents state-of-the-art research in these important areas. It is suitable for graduate students and researchers in difference equations and related topics.
Discrete-Time Dynamics of Structured Populations and Homogeneous Order-Preserving Operators
A fundamental question in the theory of discrete and continuous-time population models concerns the conditions for the extinction or persistence of populations – a question that is addressed mathematically by persistence theory. For some time, it has been recognized that if the dynamics of a structured population are mathematically captured by continuous or discrete semiflows and if these semiflows have first-order approximations, the spectral radii of certain bounded linear positive operators (better known as basic reproduction numbers) act as thresholds between population extinction and persistence. This book combines the theory of discrete-time dynamical systems with applications to pop...
Mathematics for Ecology and Environmental Sciences
Dynamical systems theory in mathematical biology has attracted much attention from many scientific directions. The purpose of this volume is to discuss the many rich and interesting properties of dynamical systems that appear in ecology and environmental sciences. The main topics include population dynamics with dispersal, nonlinear discrete population dynamics, structured population models, mathematical models in evolutionary ecology, stochastic spatial models in ecology, game dynamics and the chemostat model. Each chapter will serve to introduce students and scholars to the state-of-the-art in an exciting area, to present important new results, and to inspire future contributions to mathematical modeling in ecology and environmental sciences.
Dynamical Systems in Population Biology
Population dynamics is an important subject in mathematical biology. A cen tral problem is to study the long-term behavior of modeling systems. Most of these systems are governed by various evolutionary equations such as difference, ordinary, functional, and partial differential equations (see, e. g. , [165, 142, 218, 119, 55]). As we know, interactive populations often live in a fluctuating environment. For example, physical environmental conditions such as temperature and humidity and the availability of food, water, and other resources usually vary in time with seasonal or daily variations. Therefore, more realistic models should be nonautonomous systems. In particular, if the data in a m...
Dynamics, Games and Science
The focus of this volume is research carried out as part of the program Mathematics of Planet Earth, which provides a platform to showcase the essential role of mathematics in addressing problems of an economic and social nature and creating a context for mathematicians and applied scientists to foster mathematical and interdisciplinary developments that will be necessary to tackle a myriad of issues and meet future global economic and social challenges. Earth is a planet with dynamic processes in its mantle, oceans and atmosphere creating climate, causing natural disasters and influencing fundamental aspects of life and life-supporting systems. In addition to these natural processes, human ...
Dynamical Systems and Population Persistence
"The mathematical theory of persistence answers questions such as which species, in a mathematical model of interacting species, will survive over the long term. It applies to infinite-dimensional as well as to finite-dimensional dynamical systems, and to discrete-time as well as to continuous-time semiflows. This monograph provides a self-contained treatment of persistence theory that is accessible to graduate students. The key results for deterministic autonomous systems are proved in full detail such as the acyclicity theorem and the tripartition of a global compact attractor. Suitable conditions are given for persistence to imply strong persistence even for nonautonomous semiflows, and t...
