Complex Systems, Resilience, and Tipping Points

This interdisciplinary textbook explores how environmental and social systems respond to stress, by either adapting or tipping into crisis. It presents mathematical theory in an accessible way and connects dynamic systems with real-world data. Chapters analyse the ball and cup model, phase diagrams, bifurcations, and real-world case studies such as the Atlantic Meridional Overturning Circulation (AMOC), Arctic sea ice, ecosystem collapse, nonlinearity, feedbacks, thresholds, and resilience in both Earth and social systems. Each chapter includes questions to encourage discussion, analytical exercises to build technical skills, and multiple choice questions to reinforce learning. With clear language, vivid examples, and interactive exercises, this book equips students and instructors across science, policy, and sustainability with tools to understand and manage change in a rapidly transforming world. It is ideal for senior undergraduates, graduate students, scientists, policymakers, and professionals in environmental science, ecology, climate science, physics, economics, and public policy.