Questions tagged [stability]
Stability theory, including global stability (in dynamical systems, where it can notably be used in combination with ds.dynamical-systems)
9
questions
3
votes
0
answers
364
views
Fujita decomposition versus Zariski decomposition
Fujita decomposition: Let $\frak \pi : X \to B$ be a fibration of a compact Kahler manifold $\frak X$ over a projective curve $\frak B$ then $\pi_*\left(K_{\frak X/B}\right)=A\oplus B$ where $A$ is ...
user21574
2
votes
0
answers
101
views
Stochastic stability of "open" continuous-time stochastic systems: reference request
I'm looking for results on the stability of stochastic systems, e.g. SDEs, whose coefficients depend on a different process that is not necessarily stable. I'm calling those systems "open" here, but ...
- 1,675
12
votes
1
answer
2k
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Derived categories of singular varieties
Given my limited knowledge on derived categories, all the results on derived categories of complex of bounded sheaves are build upon smooth varieties, and people literally avoid singular case (as in ...
- 3,362
8
votes
2
answers
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views
Bounded input Bounded output stability for heat equation
This is a cross-post from Computational Science.
I am interested in proving or obtaining a counterexample to the following conjecture.
Let $\Omega\subset\mathbb{R}^d$ be a bounded open domain. Let ...
- 142
7
votes
1
answer
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views
How to study the global stability for this 3D system?
I am studying a biological system (HIV) and arrived at this simplified dynamical system:
\begin{align}
x_1' &= a_1 + a_2x_2 - a_1x_2 - a_4x_1 - a_5\frac{1+a_6x_3}{1+a_7x_3}x_1\\
x_2' &= a_5\...
- 513
5
votes
2
answers
791
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 $V(x)$ ...
- 2,682
4
votes
1
answer
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views
When does the maximal root of this polynomial have unit magnitude? Prove an inverse linear relation between parameters
Examine the polynomial
$$
x^{\tau+1}-x^{\tau}+\alpha=0\,
$$
and denote by $\left|x_{\max}\left(\tau,\alpha\right)\right|$ as the
maximal magnitude of a root of this equation. For $\tau>1$, I ...
- 876
3
votes
1
answer
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views
Lyapunov stability of linear system
Consider a linear ODE system
$$\dot x_k=\sum_{j=1}^ma_{kj}(t)x_j,\qquad k=1,\ldots, m,\quad a_{kj}(t)\in C[0,\infty).\quad (1)$$
Proposition. Suppose that $$\sup_{t\ge 0}\Big\{\int_0^t\Big(a_{kk}(...
- 31
1
vote
0
answers
258
views
Maximizing the ratio of largest eigenvalues
Let $K$ be a real stable matrix; more specifically,
$$
K=\left(\begin{array}{rrrrr}
0&1&0&\ldots&0\\
0&0&1&\ldots&0\\
\vdots&\vdots&\vdots&\ddots&\vdots\...
- 270