LAUSR

Synchronization properties of model systems containing large numbers of phase oscillators have many potential biophysical and other applications. Biophysical examples include networks of pacemaker cells in the heart and suprachiasmatic nucleus of the brain. In physical systems, the phase dynamics of high- $T_{\rm c}$ superconducting materials continue to attract attention, since systems of intrinsic Josephson junctions form natural arrays of coupled phase oscillators. As such, they have the potential to act as systems in which various exotic synchronization effects may be observed. In this paper, we make a more detailed exploration of the parameter space containing regions of spontaneous chaos synchronization in the CCJJ + DC model of intrinsic Josephson junctions. Extensive regions of phase synchronization—corresponding to the Shapiro steps with zero charge density in the S-layers—are found through numerical simulation. By computing the Lyapunov exponent spectra, we see that the spontaneous chaos synchronization occurs within certain subregions that overlap with uncharged steps in the IV-characteristics. We tried to stabilize the spontaneous chaos synchronization over a wider range of parameters, by applying a global, noninvasive, and proportional control scheme. The control is affected by applying a time-dependent phase shift to the external electromagnetic radiation, proportional to the total voltage. The effect of the control is found to be three-fold. First, it tends to broaden the current interval over which lower harmonic Shapiro steps occur. Second, it does not change the width in the current range over which the chaos synchronization occurs. Third, it makes the chaos synchronization more robust to thermal noise. The chaos synchronization we report here may be useful in any applications requiring more powerful, high-frequency, and chaotic signals, such as in secure communication.