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Stability theory, including global stability (in dynamical systems, where it can notably be used in combination with ds.dynamical-systems)

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
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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 $V(x)$ …
Ludwig's user avatar
  • 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. …
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  • 2,712
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 …
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