| Abstract: |
| Lyapunov functions are a valuable tool for the global stability analysis of nonlinear dynamical systems. However, they are notoriously difficult to find, even for ODEs, and there is no general method for constructing them. Despite this, Lyapunov functions have been found for many dynamical systems, giving a ``library of pairs:
[ dynamical system, Lyapunov function ]
In the particular case of compartmental models for the transmission of infectious disease, there has been great progress in finding Lyapunov functions over the last 20 years, expanding the library. This library can be drawn upon when exploring the stability of a dynamical system that is similar to a system for which a Lyapunov function is known.
In this lecture, I will discuss this process, including recent results. |
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