Introduction to Complex Systems

The world around us is complex. Complexity science seeks to understand how large collections of connected elements link together, forming more than just the sum of their parts. The science of complex systems is a modern, evolving field that draws from various disciplines such as physics, biology, medicine, social sciences, economics, computer science and engineering.

As it turns out, very different systems such as Earth’s climate, the stock market or neurons in the brain tend to show similar behavior when viewed through a complex systems lens. An integrated way of thinking is thus essential for a deeper understanding of the complex challenges humanity is facing. Learning about complex systems is a great way to broaden your perspective beyond your typical field of study, regardless of your scientific background.

When describing a complex system, the first step is to abstract the specific system into similar elements and the interactions between them. The question is then: how does the behavior of the system as a whole depend on the nature and structure of the interactions, as well as the properties of the individual elements? The fact that the structure of interactions itself is important has given rise to the relatively young theory of complex networks.

Sometimes the interactions lead to emergent behavior that cannot be explained by the collection of individual elements alone. How can we predict these dynamics and control complex systems in the real world? For example, complexity science studies which properties of a complex system are most vulnerable to change or what can be done to make the system more resilient. This becomes particularly important when studying critical transitions between different states, as relevant for climate tipping points, ecosystem shifts, pandemics, sociopolitical change or disruptive innovations.