Effect of parameter mismatch and noise on weak synchronization

We have numerically investigated the effect of parameter mismatch and noise on the loss of chaos synchronization in unidirectionally coupled one-dimensional maps. Through a first transverse bifurcation of an unstable periodic orbit embedded in the synchronous chaotic at-tractor (SCA), this attractor becomes weakly stable. In the regime of weak synchronization, any small parameter mismatch and noise transform the SCA into a bubbling attractor or a chaotic transient. In this case, the quantities of interest are the average interburst interval of the bubbling attractor and the average lifetime of the chaotic transient. They are found to scale with the mismatching parameter and the noise intensity. Furthermore, the scaling results for the cases of parameter mismatch and noise are quantitatively the same. We also give the theoretical background for the scaling by comparing our numerical results with the-oretical results. For the bubbling case, the maximum bursting amplitude is another quantity of interest. We discuss the abrupt increase in the maximum bursting amplitude that results from the sudden increase in the size of the absorbing area, confining the bursting, through an interior crisis. This is in contrast with the case of symmetric coupling, in which no such crisis occurs for the absorbing area