Thread: Problem in a system of ODEs View Single Post
 P: 3 Continuing to the Jacobian anyways, we arrive at $J = \left[ \begin{array}{ccc} -1 - (\bar{Y} + \bar{Z}) & -\bar{X} & -\bar{X} \\ a\bar{Y} & a\bar{X}-1 & 0 \\ a\bar{Z} & 0 & a\bar{X}-1 \end{array} \right].$ Plugging in what we know, $J = \left[ \begin{array}{ccc} -a & -\frac{1}{a} &-\frac{1}{a} \\ a\bar{Y} & 0 & 0 \\ a\bar{Z} & 0 & 0 \end{array} \right].$ This means that the trace of the Jacobian is negative, i.e. $tr(J) = -a < 0$. Also that the determinant is equal to zero. My book does not talk about what happens when the determinant of the Jacobian is zero. Any insights?