Deterministic control of CW/CCW alternation by dual-frequency injection in a heterogeneous oscillator ring

We investigate deterministic control of rotational alternation in a heterogeneous oscillator ring by means of dual-frequency injection. The rotating phase wave corresponds to a nonzero winding number and is thus regarded as a collective topological state. In the present system, the rotational dynamics is effectively described in terms of two dominant standing-wave-related collective components with distinct frequencies and nodal structures. These components are each associated with a collective phase variable, and the observed clockwise/counterclockwise alternation is governed by their relative phase dynamics. When the heterogeneity exceeds a threshold, a dynamical connection emerges between the two topological sectors, resulting in spontaneous temporal alternation of the winding number. Numerical analysis shows that dual-frequency injection selectively constrains the phase dynamics of the two standing-wave-related components, enabling deterministic control of the alternation period. The response to dual injection cannot be reduced to a single-phase description, as the resulting dynamics depends on both injection frequencies in a nontrivial and reproducible manner. Experimental results support these findings and demonstrate continuous tunability of the alternation period. These results indicate that the alternating collective state can be controlled through two interacting collective phase variables and suggest a route toward controlling directional dynamics in nonlinear oscillator networks.