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Tagged with stability ca.classical-analysis-and-odes
2 questions
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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 $V(x)$ ...
3
votes
1
answer
278
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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}(...