Assessment of cooperativity in complex systems with non-periodical dynamics: Comparison of five mutual information metrics

The Effects of Padé Numerical Integration in Simulation of Conservative Chaotic Systems

“…To summarize, our experimental study revealed not only the limitations of numerical methods based on a direct Padé approximation when simulating chaotic systems, but also opened the possibilities to construct highly nonlinear and less predictable discrete chaotic maps. Obtained models can be used as testbench systems in various statistical studies [25] or for simulation of nonstationary processes with multifractal properties. Though an accurate simulation with nonlinear integration techniques meets significant difficulties, these methods can improve the algorithms of pseudo-random number generators [26,27], making them able to avoid quasi-chaotic regimes during long-term runs.…”

“…Figure 6 illustrates the results for models obtained by nonlinear integration techniques. One can see that the solutions consequently pass through various chaotic regimes during the long-term simulation, exhibiting the phase transition behavior [25]. This variety of regimes may appear in DOPRI8 and EMP models only when values of nonlinearity parameters are changed.…”

Quantification of the Feedback Regulation by Digital Signal Analysis Methods: Application to Blood Pressure Control Efficacy

“…While according to the results of a recent study [30], Sync appears the most sensitive of various mutual synchronization indices, it has its own drawbacks, including high sensitivity to any (including random) variations in the analyzed signals, that requires seeking for more robust alternatives that would respond more specifically only to significant variations, although typically at the cost of their lower sensitivity.…”

“…Like in the previous method, in order to estimate the time delay stability coefficient for an entire record, the TDS value is determined as the fraction of the time delay stability episodes in the total record duration. Similarly, the starting set of the parameters used in this study follows the results of a recent simulated data based investigation [30].…”

“…While in most cases relation between rhythms with certain quasi-periodic structure is studied, such as breathing cycles modulating heartbeat cycles, we go beyond that and, while following conceptually similar methodology, modify the synchronization analysis methodology to suite the blood pressure-pulse interval analysis that both exhibit rather stochastic behavior, as indicated below. Particular mutual synchronization metrics used here follow a recent study where their performance has been validated using simulated datasets with non-periodic structure and correlation patterns reminiscent to those typically observed in physiological signals [30].…”