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 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.