Unpredictability of Iteration Destination in an Integrate-and-Fire Circuit

Based on our previous study that discovered a new mechanism of the riddled-like basin appearance in piecewise continuous and noninvertible links of two conservative mappings, and the mechanism being the mixing of different attraction basins on a fat-fractal set, which was addressed as the forbidden region net Phys. Rev. E 72 (2005) 025201(R), we show numerically that the riddled-like attraction basins and the new mechanism appear in an integrate-and-fire circuit that can be described by piecewise continuous and noninvertible links of two dissipative mappings. This leads to the fact that vast increase of the precision of the initial condition results in practically no improvement in predictability of the iteration destination. Predictability is usually characterized by examining how error probability in the prediction, f(ε), scales with the precision ε under the initial condition. Typically, f(ε) ～ ε^α with 0 ≤ α ≤ 1 being the uncertainty exponent. For riddled-like basins, α should be zero, which is in good agreement with the numerical simulation results.