Short Wavelength Bifurcations and Size Instabilities in Coupled Oscillator Systems

We report the presence of short wavelength bifurcations from synchronous chaotic states in coupled oscillator systems. The bifurcations immediately excite the shortest spatial wavelength mode present in the system as the coupling between the oscillators is increased beyond a critical value. An associated size instability places an upper bound on the number of oscillators that can support stable synchronous chaotic oscillations; an exact expression is given for the upper bound. Results are demonstrated with numerical simulations and electronic circuits.