Phase Synchronization of Nonidentical Light-Sensitive Belousov−Zhabotinsky Systems Induced by Variability in a High−Low Illumination Program

Phase synchronization of two systems with different dynamical parameters driven by a common external signal is studied using a model of the photosensitive Belousov−Zhabotinsky reaction. Complex dynamics, including chaos, arise when the external light intensity is periodically switched between two levels. Two dynamical conditions are investigated here: (a) the two systems are driven between two limit cycles and (b) both systems are driven between excitable and oscillatory states. Phase synchronization is achieved with both Gaussian-distributed and dichotomous noise when the random variation is added to the duration of the periodic forcing. In the case that noise is added to the intensity of the periodic forcing, perfect phase synchronization is achieved with dichotomous noise, whereas only transient synchronization is observed with Gaussian-distributed random variation. Studies with correlated noise show that the compound system may have two attractors, one corresponding to the phase synchronized state an...