Author Topic: Type and Stability of Origin  (Read 478 times)

Chenxi Lai

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Type and Stability of Origin
« on: November 25, 2014, 11:40:15 PM »
Hi Pro,
1)What's the difference between an asymptotic stable point and stable point?
2)What is an intermediate point?
3)Why the type of origin sometimes depends on the linearization of the system of equation?

Victor Ivrii

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Re: Type and Stability of Origin
« Reply #1 on: November 26, 2014, 05:48:55 AM »
Hi Pro,
1)What's the difference between an asymptotic stable point and stable point?
2)What is an intermediate point?
3)Why the type of origin sometimes depends on the linearization of the system of equation?

Hi Bro,
1) Stationary point $\mathbf{x}_0$ is stable if for arbitrary small vicinity $U$ of it there is such small vicinity $V$ such that every solution $\mathbf{x}(t)$ with $\mathbf{x}(0)\in V$ remains in $U$ for all $t>0$.

Stationary point $\mathbf{x}_0$ is asymptotically stable if it is stable and  every solution $\mathbf{x}(t)$ with $\mathbf{x}(0)\in V$ tends to $\mathbf{x}_0$ as $t\to +\infty$.

2) No idea where you got this

3) No idea what do you mean

Kelly Yang

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Re: Type and Stability of Origin
« Reply #2 on: December 02, 2014, 12:45:23 PM »
Hi Chenxi,

For question 2, I think you mean 'Indeterminate'. If I recall correctly, it occurs when the stability cannot be determined in the Locally Linear System, when the eigenvalues are complex with zero real value (i.e. +- i b)