Exploiting dynamical symmetry in coupled nonlinear elements for efficient frequency down-conversion

The rich dynamical behavior stemming from unidirectional coupling in a single array of overdamped nonlinear elements has, recently, been extensively studied. By adjusting control parameters, one obtains regimes of oscillations with a frequency that scales in a characteristic way with the control parameter. With an external time-sinusoidal driving signal, a richness of synchronized (to the drive frequency or its subharmonics depending on the control parameter) dynamical behavior ensues. Including M > or = 2 arrays with a suitably chosen cross coupling has also been shown to lead to multifrequency patterns in the emergent dynamics. Here, we consider this arrangement and demonstrate that, under the appropriate conditions, the oscillation frequency of each successive array decreases by a rational factor with increasing M . This frequency down-conversion, obtainable without a heterodyning signal, affords the promise of very efficient signal processing in a variety of applications wherein, currently, the frequency down-conversion stage typically involves multistep processes with complicated and (often) noisy circuitry.