Asaf pointed out that stability-theory now exists. Recall what was said about it last September:
If you use stability-theory, people will use it for stability in GIT theory, stability in other numerical algorithms, stable reduction in elliptic curves, and other things I'm not thinking of right now. [...] – David Speyer Sep 14 '14 at 16:53
... and even more folks might assume that "stability theory" is about "stable homotopy groups of spheres", "stably homeomorphic manifolds", "structural stability" in general dynamical systems, etc. [...] – studiosus Sep 14 '14 at 17:09
Let's see what happened in practice. The tag was created in April, for the question #1 on the list (model-theoretic concept of stability). No tag excerpt or wiki was written. Subsequently, the tag was used 20 times — for anything but model theory. Topics include: ODE, PDE, discrete dynamical systems, difference equations, numerical methods for ODE/PDE, numerical linear algebra.
- (stability-theoretic) ¨weakly normal groups" are closed under subgroups
- Schur-Cohn Stability Criterion
- Is a feedback system with an unstable component and the other component being zero internally stable?
- Lyapunov equation for stability analysis - what's the point?
- Changing direction of Nyquist plot with PID-controller
- What does a 3D periodic solution of a differential equation look like?
- Backwards Stability of systems
- What is 'bursting' in least squares estimation, and what causes it?
- Theorem to show trajectories of differential equations are close after small change to initial condition
- Example of BIBO stable system that is not internally stable
- Stability using lyapunov function
- How to interpret complex eigenvectors of the Jacobian matrix of a (linear) dynamical system?
- Frequency Response of unstable systems
- does an exponential bound on a Lyapunov candidate implies asymptotic stability?
- How do i show stability of fixed points of this two.dimensioanl system:f(x,y)=(y,y²−x²)f(x,y)=(y,y²−x²)?
- Finding a Ljapunov function for discrete dynamical system with 3 variables.
- Stability of Gauss elimination [closed]
- Definition of positive definite function
- Stability in partial differential equations
- Stability of non-homogeneous and non-autonomous first-order difference equation
- Bounded Input Bounded Output stability for Heat Equation (Cross-Post from Sci-comp stackexchange)
Sigh. I will retag as stability-in-odes where appropriate. (That tag does get used, 60+ times by now). Questions without an answer:
Should the tag stability-in-odes be renamed as stability-of-solutions, to capture PDE and difference equations/dynamical systems?
Should stability-theory remain, and if so, what should it mean?