MAT244-2014F > MAT244 Math--Lectures

Type and Stability of Origin

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**Chenxi Lai**:

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**:

--- Quote from: Chenxi Lai 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?

--- End quote ---

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**:

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)

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