Directed ratchet transport in starlike networks of driven damped pendula by localized symmetry-breaking-inducing excitations

We study the effectiveness of locally controlling the breakage of a significant space-time symmetry by zero-average periodic excitations at inducing and suppressing directed ratchet transport (i.e., that induced without an applied net bias) and chaos in starlike networks of driven damped pendula. While the emergence of chaos mainly depends upon the impulse transmitted by the periodic excitations, directed ratchet transport does upon a subtle balance between energy transmitted through the pendula via excitations' impulse and degree of symmetry breaking, thus defining a physical criticality scenario. Optimal enhancement of directed ratchet transport is found to occur when the waveform of the periodic excitation matches as closely as possible to a universal waveform when all nodes are homogeneously driven. In the case of networks with heterogeneous distributions of the symmetry breaking, the net ratcheting effect of increasing the effective breakage by periodic excitations acting on a number of particular nodes strongly depends upon their number and degree of connectivity as well as the coupling strength, while showing self-organized criticality with respect to the maximum strength of directed ratchet transport.