Rössler attractor

Example

Let $a, b, c$ be real parameters. The Rössler system is the autonomous system in $\R^3$ $$x' = -y - z, \qquad y' = x + a y, \qquad z' = b + z (x - c).$$ Otto Rössler proposed it in 1976 with $a = b = 0.2$ and $c = 5.7$. For these values, numerical solutions approach a bounded set with a folded band shape, the Rössler attractor.

The equilibrium points are found as follows. The equation $y' = 0$ gives $x = -a y$, and $x' = 0$ gives $z = -y$. Then $z' = 0$ becomes $a y^2 + c y + b = 0$. So for $a \ne 0$ and $c^2 > 4ab$ there are exactly two equilibria, with $y = \left(-c \pm \sqrt{c^2 - 4ab}\right)/(2a)$.