Synchronizing Solvable Chaotic Oscillators

We present the synchronization of two chaotic systems. These systems consist of solvable chaotic oscillator circuits operating at 10kHz with similar parameters. Although many chaotic systems have been synchronized, few instances of synchronized solvable chaos have been reported in hardware. Here, we use the analytical solution of solvable chaos to quantitatively measure the effect of coupling on the synchronized chaotic systems. The resulting oscillators are characterized by their time-series, return maps, phase portraits and finally by their closed-form analytical solutions. We subsequently synchronize these systems via bidirectional resistive coupling. Synchronization of these types of systems enables phase synchronization applications and clock recovery in popular ranging and secure communication schemes such as bistatic radar, chaotic mask and chaos shift keying (CSK).