Sandstede's Model.

Consider the system [#!Sa:95b!#]

$$\begin{array}{rcl} \dot{x} & = & a \, x + b \, y - a \, x^2 +... ...\, y + \alpha \, \beta \, (x^2 \, (1-x) - y^2) \par \end{array}$$ (21.1)

as given in the file san.f. Choosing the constants appearing in (21.1) appropriately allows for computing inclination and orbit flips as well as non-orientable resonant bifurcations, see [#!Sa:95b!#] for details and proofs. The starting point for all calculations is $a=0$, $b=1$ where there exists an explicit solution given by

$$(x(t),y(t),z(t)) = \left( 1 - \left(\frac{1-e^t}{1+e^t}\right)^2 , 4 \, e^t \, \frac{1-e^t}{(1+e^t)^3} , 0 \right).$$

This solution is specified in the routine STPNT.