The one data structure that crops up again and again when looking at complex systems is the graph. Nodes on the graph represent the components and elements like state variables (e.g. population, resources, temperature, servers and clients, etc.) of the system, and edges between nodes represent interconnections, e.g. flows of matter, energy or information between nodes.
A good introduction to this way of looking at the world is "Thinking in Systems: A Primer" by Donella Meadows. Important concepts include analyzing systems to determine their relative robustness or fragility under stress, the nature of the feedback loops in the system (possibly some nodes are connected by partially directed edges, so flows in one direction are easy but not in the other), what kind of temporal delays matter the most (e.g. how long does it take between creating a change and seeing the result of that change), and so on.
Given the natural utility of graphs in modeling systems, it's really a bit strange that graph theory really only developed in the 20th century, with some minor exceptions like Euler and Kirchhoff. It's interesting to think about an alien civilization whose mathematics began with graphs and how it might have developed.
A good introduction to this way of looking at the world is "Thinking in Systems: A Primer" by Donella Meadows. Important concepts include analyzing systems to determine their relative robustness or fragility under stress, the nature of the feedback loops in the system (possibly some nodes are connected by partially directed edges, so flows in one direction are easy but not in the other), what kind of temporal delays matter the most (e.g. how long does it take between creating a change and seeing the result of that change), and so on.
Given the natural utility of graphs in modeling systems, it's really a bit strange that graph theory really only developed in the 20th century, with some minor exceptions like Euler and Kirchhoff. It's interesting to think about an alien civilization whose mathematics began with graphs and how it might have developed.