06.01 Pendulums and Phase Spaces - Beyond Networks: The Evolution of Living Systems

Module 6 of "Beyond Networks" dives into dynamical systems theory, introducing its approach and its fundamental aims and concepts without going too much into the technical details. Lecture 1 introduces the basic notion of flow using the linear pendulum as an example system. A dynamical system is defined by its flow, the totality of its trajectories. I show how we can derive the flow of a system by drawing its phase portraits based on empirical observation. The flow tells us what a system can do. It is exactly in this way that dynamical systems contribute to mechanistic explanation.
I've borrowed this introduction to dynamical systems from my long-term collaborator Nick Monk. If it stands out as being better than the rest of the lecture series, that's entirely his fault!
If you are interested in learning more about dynamical systems theory, please read Steven Strogatz brilliant textbook "Nonlinear Dynamics and Chaos" (now in its 2nd edition, published in 2014). It takes a very accessible visual approach to explain the concepts of the field. An exceptional pedagogical achievement, outstanding among maths textbooks. I highly recommend it!