Introduction to Complexity Science

Overview

This course explores the features of complexity science. Our world is connected by an abundance of complex systems. Across all levels of organizations from physical, biological world to the social world, we may think of the connectivity between individual elements and how they interact and influence each other. For example, how humans transmit pandemics within a group, how cars interact in the traffic system and how networks connect in governmental organizations. Although these systems are diverse and different, they have surprisingly huge features in common. In the past several decades, the study of complexity science has been increasing. It is widely acknowledged that an innovative, integrated and analytical way of thinking is essential for understanding the complex issues in the human societies. In this course, we will aim to give everyone a comprehensive introduction of the complex systems, to talk about the resilience, robustness and sustainability of the systems and to learn basic mathematical methods for complex system analysis, for example regime shifts and tipping points, the agent-based modelling, the dynamic and network theories. Most importantly, we will implement the theories into practical applications of cities and health to help students gain practice in complex systems way of thinking.

Syllabus

Course Overview and Week 1: Introduction to Complex Systems

An overview of what is covered in the first topic: an introduction to complex systems, explaining how complexity science has evolved, how it has been applied in society, and why it is important to gain a basic understanding of complex systems. Like for all sciences, complexity science is not a spectators' sport. After learning models and methods from the lectures, you will need to try some of these out to develop a practical feel for what they mean and what they can do. This is where the Jupyter Notebook exercises come in. In this course week, we will try out two Jupyter Notebook exercises, on: (1) the Nagel-Schreckenberg model of vehicular traffic, and (2) the Game of Life.

Week 2: Robustness, Resilience, and Sustainability

In this 2nd topic, we look at how robustness, resilience and sustainability can be defined for complex systems, and some case studies that showcase these attributes.

Week 3: Regime Shifts and Tipping Points

In this third topic, we move on to looking at regime shifts and tipping points and their applications in forecasting.

Week 4: Introduction to Agent-Based Modeling

Next, we look at Agent-Based Modeling - what it is, how it works, why it is used and how to use it. We then try a Jupyter Notebook exercise on Schelling’s Segregation Model.

Week 5: Introduction to Static Complex Network

Lastly, we look at complex networks and their attributes before looking at different network models. We end this topic with a Jupyter Notebook exercise on epidemics on complex networks.