Modeling Practical Problems in Complex Systems

Complex systems-characterized by self-organization, emergence, and profound non-linearity-govern everything from global financial markets to ecological stability. Navigating this complexity requires a unified mathematical framework that moves beyond traditional linear models. This book provides that essential toolkit, offering a robust, interdisciplinary approach to simulation, forecasting, and management across engineering, economic, and environmental fields. What sets this volume apart is its integration of ecological and evolutionary perspectives with quantitative approaches to simulate, forecast, and manage complexity in diverse domains including finance, agriculture, and environmental science. Throughout the book, readers will find practical examples, case studies, and advice on how to apply scientific modeling techniques to solve real-world problems. It also presents insights into best practices and strategies for using modeling and simulation effectively in various fields. This book is an indispensable resource for researchers, quantitative analysts, and advanced students in complexity science, evolutionary economics, quantitative finance, and ecological modeling. It provides the theoretical depth and practical, data-driven methods necessary to analyze and manage the world's most challenging complex systems. Key Features - Contains an in-depth treatment of nonlinear dynamics and evolutionary processes as foundational frameworks for understanding complex system behavior. - Provides applications of dynamical systems to real-world problems in ecology, environmental sciences, economics, and financial markets, emphasizing the parallels between biological evolution and market competition. - Presents illustrations through a variety of case studies, featuring practical applications to S&P 500 stock dynamics, optimization of livestock production, and forecasting the collapse of threatened biomes.

Hugo Fort is a professor at the Department of Physics of the Faculty of Sciences at the University of the Republic (Montevideo, Uruguay) and the Head of the Complex Systems Group. After earning his PhD in Physics from the Autonomous University of Barcelona in 1994, he conducted research in quantum field theory. Since 2001, his scientific interests have evolved from theoretical physics to complex systems and mathematical modeling applied to problems in biology, with a focus on ecology and evolution. Professor Fort is currently involved in several international research collaborations pursuing user-inspired basic science applied to problems of production optimization and conservation. He has written two books, Ecological Modelling and Ecophysics (2020) and Forecasting with Maximum Entropy: The interface between physics, biology, economics and information theory (2022); he is also the author of over 100 articles in scientific journals and book chapters in diverse fields including agricultural sciences, applied mathematics, biology, ecology, physics, and social sciences modeling. Professor Fort has taught several courses in mathematical modeling, complex systems, nonlinear dynamics, and statistical physics. He has also been collaborating on different projects with national agencies as a senior scientific consultant.

Chapter 1 COMPLEX SYSTEMS AND PREDICTABILITY Chapter 2 NONLINEAR DYNAMICS Chapter 3 EVOLUTIONARY DYNAMICS Chapter 4 POPULATION DYNAMICS APPROACHES TO ECONOMICS AND FINANCE Chapter 5 A PROBABILISTIC FRAMEWORK FOR PREDICTABILITY BASED ON INFORMATION THEORY Chapter 6 FORECASTING METHODS FOR COMPLEX SYSTEMS Chapter 7 CONTROL AND MANAGEMENT OF COMPLEX SYSTEMS: PRACTICAL EXAMPLES IN AGRICULTURE & ENVIRONMENTAL SCIENCE Chapter 8 THE LIMITS OF PREDICTABILITY THROUGH MATHEMATICS AND COMPUTATION