Generic behavior of coupled oscillators

There exist a number of interesting physical problems, such as the ac-driven, dc SQUID (superconducting quantum interference device) or convection in conducting fluids, which can be described by the dynamics of driven coupled oscillators. In order to study their behavior as a function of coupling strength and nonlinearity, we have considered the dynamics of two coupled maps belonging to the same universality class as the oscillators. We have analytically determined some of the parameter values for which they exhibit locked states as well as bifurcations into aperiodic behavior. Furthermore, we found a set of codimension-two bifurcations into quasiperiodic orbits near which the rotation number becomes vanishingly small. These bifurcations are characterized by the existence of periodic regimes interrupted by episodes of phase slippage. Finally, we show the effect of thermal fluctuations on the bifurcation diagram by computing the Lyapunov exponent in the presence of external and parametric noise.