The characters of riddled basins in coupled chaotic synchronized maps with additive noises

In real systems, because of the inevitable noise, a chaotic synchronized attractor A will turn into a metastable attractor A' with an average lifetime <tau>. We analyze a two-dimensional coupled map with additive noises and find analytically that the riddled basin of A' will disappear when <tau> < 2 T and can only be observed qualitatively when <tau> > 2 T, where T is the duration of an experiment. According to the characters of the riddled basin without noises, it is found that the riddled basin will turn into not only a temporal riddled basin but also a regular fractal basin. This result is universal in two-dimensional coupled chaotic synchronized maps, and the further numerical calculations can also confirm this point.