Effect of measuring noise on scaling characteristics in the dynamics of coupled chaotic systems

We study the scaling features in the evolutionary dynamics of two coupled chaotic systems based on the sequences of return times into a Poincaré section, contaminated with additive (measuring) noise. Using three models of chaotic systems: the Rössler oscillator, the Lorenz system, and the nephron model, and the detrended fluctuation analysis (DFA) as an approach for data processing, we demonstrate that the anti-correlated sequences of return times of synchronous motions show a higher sensitivity to measuring noise than the positively correlated series of return times of asynchronous oscillations. This conclusion is confirmed by the results for various oscillatory regimes in all models considered.