Homoclinic chaos in a laser: synchronization and its implications in biological systems

Phase synchronization of a CO₂ laser with feedback, exhibiting homoclinic chaos, is realized by a tiny periodic perturbation of a control parameter. The deviations of the modulation frequency from the optimal one induce phase slips, thus yielding an imperfect phase synchronization. Based on the information of these phase slips, the modulation frequency can be readjusted until the phase slips are eliminated. In this way, a control loop which detects the phase slips provides an adaptive tracking of the natural frequency of the dynamical system. Moreover, we have shown that the system's susceptibility is largest when a periodic impulsive perturbation is applied near the saddle focus.