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Results tagged with stability
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user 62673
Stability theory, including global stability (in dynamical systems, where it can notably be used in combination with ds.dynamical-systems)
1
vote
0
answers
37
views
Attractivity of a system with state-dependent transitions
Let $A\in\mathbb{R}^{n\times n}$ and consider the following dynamical system:
$$
\frac{\mathrm{d}x(t)}{\mathrm{d}t} = -x(t)+\max\{0,Ax(t)\}, \ \ \ \ x(0)\in\mathbb{R}^n,
$$
where $\max\{\cdot\}$ acts …
- 2,712
5
votes
2
answers
816
views
Conditions for convergence to non-isolated fixed points
Consider a dynamical system of the form
$$
\dot{x}=f(x), \quad x\in X,
$$
and assume that the system possesses a set of non-isolated fixed points. Suppose moreover that there exists a Lyapunov $V(x)$ …
- 2,712
2
votes
1
answer
134
views
On local attractivity of a coupled non-linear differential equation
This could be due to the fact that I'm rather new on this kind of (local) stability problems. So I would be enormously grateful in hearing any comment/criticism/suggestion from you. …
- 2,712
7
votes
1
answer
924
views
(In)stability of a two-dimensional dynamical system
one could exploit Floquet theory to express the transition matrix of the system in the form $P(t)e^{Rt}$ where $P(t)$ is a periodic function and $R$ a constant matrix, whose eigenvalues determines the stability …
- 2,712