Case when Dynamical System X'=AX has repeated eigenvalues of A|(0,0) is stable/unstable for -ve /+ve
Автор: Calculus Craze
Загружено: 2022-10-05
Просмотров: 462
Описание:
In this video, we will consider the case when A has repeated real eigenvalues. One simple case occurs when A is a diagonal matrix or upper triangular with a12=1.
Note that, if λ is -ve, each term in this solution tends to 0 as t → ∞. Hence all solutions tend to (0, 0) as t → ∞.
When λ is positive , all solutions tend away from (0, 0). . In fact,
solutions tend toward or away from the origin in a direction tangent to the
eigenvector (1, 0).
#mathematics #sukkuriba #dynamicalsystems #Mathforyou
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