Questions tagged [stability]
Stability theory, including global stability (in dynamical systems, where it can notably be used in combination with ds.dynamical-systems)
14 questions from the last 365 days
1
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63
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Stability Problem in a Nonlinear Dynamical System
Consider the nonlinear dynamical system given by the following differential equations
\begin{cases}
\dot{x} = y, \\
\dot{y} = x - x^3 - \gamma y + \delta x^2 y.
\end{cases}
I want to demonstrate that, ...
- 31
1
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0
answers
52
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Stability of Euler discretization
I am looking at the discretization of an ODE:
$$x_{n+1} = x_n + \alpha f(x_n),$$
where $x_n\in R^d$ and $f$ is continuously differentiable and such that $f(0)=0$ and $f'(0)$ is Hurwitz (i.e., the real ...
- 562
5
votes
1
answer
211
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Stability of ODEs with polynomial nonlinearity
Consider the following ODE system:
$$
x′=f(x)\iff
\begin{pmatrix}
x_1^\prime \\
\vdots\\
x_k^\prime\\
\vdots\\
x_n ^\prime
\end{pmatrix} =
\begin{pmatrix}
f_1(x) \\
\vdots\\
f_k(x)\\
\vdots\\
f_n(x)
\...
- 807
3
votes
0
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107
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Stability of a nonlinear dynamical system with non-elementary dynamics
I am trying to prove stability and get a non-asymptotic upper bound on the convergence rate of a nonlinear discrete-time dynamical system, whose dynamics are stated in terms of the (non-elementary) ...
- 31
2
votes
1
answer
154
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$R^1\Gamma = 0$, and the Mumford stability
Let $S$ be a smooth projective surface with an ample divisor $H$ so that $K_S \cdot H < 0$.
Let us consider the Mumford slope $\mu(E) = \frac{H \cdot c_1(E)}{\operatorname{rk}(E)}$ on $\...
2
votes
0
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48
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Characterization of multifunctions with globally asymptotically stable minimal invariant sets
Let $(X, d)$ be a compact connected metric space. Consider a compact-valued upper semicontinuous multifunction $F: X \rightrightarrows X$. The reachable set $R[x]$ of $F$ from $x\in X$ is defined as:
...
- 111
1
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0
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53
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The Frobenius integrability of distrbution and Hyers–Ulam–Rassias stability
Let $M$ be a compact Riemannian manifold. The norm of vector fields are computed with respect to the metric. Moreover for every distribution $D$, the orthogonal projection on $D$ is ...
- 356
0
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0
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25
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Numerical computation of spectral abscissa of operator
I would like to numerically compute the spectral abscissa of an unbounded linear operator $A$ on a Hilbert space. To give you an idea my operator has the form:
$$Af(x,y) = a(y) \partial_x f(x,y) - b(x)...
- 143
2
votes
0
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56
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Stability on manifold with boundary
Let $(X,\partial X)$ a smooth Kahler manifold with boundary, i.e. the interior of $X$ is Kahler, Donaldson proved that:
Given a smooth vector bundle $E$ over $X$ such that $E$ is holomorphic over the ...
- 395
1
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0
answers
63
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Identifying Saddle-node bifurcation of a 3D system of ODEs
I am trying to understand and prove the results shown in the following article. However, I am stuck at a point where it is stated that saddle-node bifurcation of periodic orbits occurs at ...
- 53
0
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0
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105
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Proving Hopf bifurcations for 3D system
I am working with a 3D continuous system of ODEs. I have found Hopf bifurcation numerically for a certain value of parameter. However, I want prove it analytically. Is it enough to show that the ...
- 53
2
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0
answers
60
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Identifying bifurcation
[![enter image description here]] 1]1I am trying to analyze the bifurcation of a 3D continuous model. For a certain range of parameter values, the origin is always an unstable point, whereas the ...
- 53
2
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0
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65
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Where can I find resources for a paper "Stability analysis of a novel DDE of HIV CD4+ T-cells"?
I am currently working on a the paper [NND]:
Question:
On page 4, equation 6 introduces a concept related to the infection rate within the context of the HIV model. Unfortunately, the paper does not ...
- 232
2
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1
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102
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Norm bound in simultaneous stability to semidefinite program
In the context of robust control, I remember hearing that the two following problems are equivalent.
Find $P \succ 0$, such that $A P + P A^{\top} \prec 0$ for all $A \in \mathscr{A}$ where $$\...
- 275