From the Hamiltonian corresponding to a pendulum with a rotating point of suspension, this Demonstration calculates the phase portrait showing chaotic dynamics, whose most notable feature is the existence of a separatrix.

where is the frequency of small oscillations for the unperturbed case, is a dimensionless parameter of perturbation chosen to be small, and is the frequency.

Reference

[1] G. M. Zaslavsky, Physics of Chaos in Hamiltonian Systems, 2nd ed., London: Imperial College Press, 2007 pp. 14–17.