Norton Santiago
12/27/2023 · High School
(b) let the systen of differential equations be given by \[ \frac{d x}{d t}=-x y+x(1-x) \] \[ \frac{d y}{d t}=-3 x^{2} y+2 y\left(1-\frac{y^{2}}{2}\right) \] (i) Determine the \( x-i \) socines and \( y \) - isoclines and tee signs of \( \frac{d z}{d t} \) and dy/dt. (ii) Determine the equilibrium points of the system.
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The \(x\)-isoclines are \(x = 0\) and \(y = 1 - x\). The \(y\)-isoclines are \(y = 0\), \(y = \sqrt{2 - 3x^2}\), and \(y = -\sqrt{2 - 3x^2}\). The equilibrium points are \((0, 0)\), \((0, \sqrt{2})\), \((0, -\sqrt{2})\), and \((1, 0)\).
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