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8.3: Двовимірні біфуркації
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Ми використовуємо $r^2 = x^2 + y^2$ ,\[\begin{aligned}\overset{.}{x}&=\overset{.}{r}\cos\theta -\overset{.}{\theta}r\sin\theta \\ &=(\mu r-r^3)\cos\theta -(\omega +br^2)r\sin\theta \\ &=\mu x-(x^2+y^2...Ми використовуємо $r^2 = x^2 + y^2$ , $\begin{aligned}\overset{.}{x}&=\overset{.}{r}\cos\theta -\overset{.}{\theta}r\sin\theta \\ &=(\mu r-r^3)\cos\theta -(\omega +br^2)r\sin\theta \\ &=\mu x-(x^2+y^2)x-\omega y-b(x^2+y^2)y \\ &=\mu x-\omega y-(x^2+y^2)(x+by); \\ \overset{.}{y}&=\overset{.}{r}\sin\theta +\overset{.}{\theta}r\cos\theta \\ &=(\mu r-r^3)\sin\theta +(\omega +br^2)r\cos\theta \\ &=\mu y-(x^2+y^2)y+\omega x+b(x^2+y^2)x \\ &=\omega x+\mu y-(x^2+y^2)(y-bx).\end{aligned}$