Aliza J.

asked • 08/20/20

Jacobian matrix of a nonlinear system

LaTeX: \left[\begin{array}{rrr}
2 \, x \, \sin y & & (x^2 + 1) \, \cos y\\
\\
- \sin (x + \frac{\pi}{2}) \cdot ( y^2 + 1) && 2 \, y \, \cos ( x + \frac{\pi}{2})
\end{array}\right] 

is a Jacobian matrix of a nonlinear system LaTeX: \left\{\begin{array}{l}
x^{\prime}(t) = f(x(t), \, y(t))\\
y^{\prime}(t) = g(x(t), \, y(t))
\end{array}\right.  with a list of critical points.

From below choices, select all critical points  that are classified as stable using the above Jacobian matrix.

A.) LaTeX: (- \frac{\pi}{2}, \, \frac{\pi}{2})

B.) LaTeX: (0, \, 0)

C.) LaTeX: (\pi, \, 0)

D.) LaTeX: (0, \, \pi)


1 Expert Answer

By:

C H. answered • 08/20/20

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