Location: Gilman 132
When: April 13th at 1:30 p.m.
Title: Relations of Dynamical Systems through their Maps
Abstract: Stability is a fundamental notion in dynamical systems and control theory that, traditionally understood, describes asymptotic behavior of solutions around an equilibrium point. This notion may be characterized abstractly as continuity of a map associating to each point in a state-space the corresponding integral curve with specified initial condition. Interpreting stability as such permits a natural perspective of arbitrary trajectories as stable, irrespective of whether they are stationary or even bounded. While methods exist for recognizing stability of equilibria points, such as Lyapunov’s first and second methods, such rely on the state’s local property, which may be readily computed or evaluated because solutions starting at equilibria go nowhere. Such methods do not obviously extend for non-stationary stable trajectories. We present a result which guarantees that a class of maps of dynamical systems preserves stability. Such result is illustrative of a principle that maps (in a category) are probes for understanding. With this as motivation, we will touch on more general work that maps between subsystems interconnect into maps between networks.
Zoom link: https://wse.zoom.us/j/95738965246