Fizaa A.

asked • 08/12/20

Find all  critical point(s) of the following system

Find all  critical point(s) of the following system:

LaTeX: \left\{\begin{array}{l}
x^{\prime}(t) = (y - 2) \, (2 x \, + \, y - \alpha)\\
y^{\prime}(t) = (x- 4) \, (x + 2 y - \beta)
\end{array} \right. 

Here LaTeX: \alpha, \, \beta   are constants.   

Find the general expression of its Jacobian matrix and simplify its each entry as much as possible. 

Determine a pair of values for LaTeX: \alpha, \, \beta     so that at least one of the critical points is a saddle unstable OR an ellipse stable. Justify your answer. 

Please show all steps

1 Expert Answer


C H. answered • 08/17/20

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