The idea of this book is to demonstrate the tendency of modern research in mathematical ecology using the optimal control theory and game-theoretic methods. The book introduces the modelling of environmental systems through conceptual game-theoretic models, showing the importance of the equilibrium behavior under resource extraction. Using discrete and continuous models of biological and physical processes, the behavior of ecological-economic systems is represented by models with analytic or numerical solutions. A range of mathematical methods including analytic and approximate methods for equilibrium definition, cooperative and collective behavior determination are used to explore such models. The main feature of the presented investigations is characterised by time consistent, stabilised, collective and cooperative concepts in ecological-economic systems. This book is recommended for researchers and post-graduate students of management, economic and in the applied mathematics departments.

The most adequate tool of synthesis of the heterogeneous notions, concepts and methods is their mathematical formalisation which provides a common language of the description and analysis. That is the reason why the concept of sustainable management is presented in this book on the base of mathematical modelling. Applied mathematics must use mathematical models and methods of their analysis for description of real systems and processes and connected practical problems. The results of an applied mathematical research lie beyond mathematics and belong in this case to the problems of sustainable management. The main value of the strict statements received by means of applied mathematics lies in the possibility of their interpretation and consequent usage in applied domains.