In many cases understanding the bifurcations of a dynamical system dependent on is challenging. Another approach is offered, which views as independent variable, and the control parameter as dependent. The system
at a fixed point x^_ can be rewritten to
\beta = \frac{x^_}{\tanh x^_}and yields pairs of (x^_, \beta) that can be plotted to receive the bifurcation diagram of the system containing all fixed points automatically.