Synchronizing a chaotic laser by injecting a chaotic signal with a frequency offset

It has been theoretically proven that a chaotic laser driven by an injected signal derived from a similar chaotic master oscillator working at a slight frequency offset operates in a new mode of synchronization. There is a certain relationship between average laser fields, which has been approximately calculated in an explicit form, and instantaneous fields form an attractor about the point defined by these average values, with a relatively small spread in the phase trajectories around it. It has been shown that such a configuration can be used in transmitting confidential information.