Symmetry breaking in a driven and strongly damped pendulum

We examine the conditions for appearance of a symmetry breaking bifurcation in damped and periodically driven pendulums in the case of strong damping. We show that symmetry breaking, unlike other nonlinear phenomena, can exist at high dissipation. We prove that symmetry breaking phases exist between phases of symmetric normal and symmetric inverted oscillations. We find that symmetry broken solutions occupy a smaller region of the pendulum's parameter space in comparison to the statements made in earlier considerations [McDonald and Plischke, Phys. Rev. B 27, 201 (1983)]. Our research on symmetry breaking in a strongly damped pendulum is relevant to an understanding of the phenomena of dynamic symmetry breaking and rectification in pure ac driven semiconductor superlattices.