ABSTRACT
The analysis of stability of ODE systems aims at characterising the behaviour of solutions to these systems under small changes of the data of the ODE model. Furthermore, it addresses the asymptotic behaviour of solutions corresponding to different values of the initial conditions, and the existence of limit cycles. In this chapter, the main tools of linearisation and eigenvalue analysis and the method of Lyapunov are discussed and applied to investigate models of population dynamics and the Lorenz model, and to explore the phenomenon of synchronisation.
