Improvement of the local prediction of chaotic time series

Characterization of complexities in combustion instability in a lean premixed gas-turbine model combustor

We characterize complexities in combustion instability in a lean premixed gas-turbine model combustor by nonlinear time series analysis to evaluate permutation entropy, fractal dimensions, and short-term predictability. The dynamic behavior in combustion instability near lean blowout exhibits a self-affine structure and is ascribed to fractional Brownian motion. It undergoes chaos by the onset of combustion oscillations with slow amplitude modulation. Our results indicate that nonlinear time series analysis is capable of characterizing complexities in combustion instability close to lean blowout.

Short-term prediction of dynamical behavior of flame front instability induced by radiative heat loss

We apply nonlinear forecasting to the time series of the flame front instability induced by radiative heat loss to test for the short-term predictability and long-term unpredictability characteristic of deterministic chaos in flame front instability. Our results indicate that the flame front instability represents high-dimensional chaos generated via the period-doubling cascade process reported in our previous study [H. Gotoda, K. Michigami, K. Ikeda, and T. Miyano, Combust Theory Modell. 14, 479 (2010)], while its short-term behavior is predictable using a local nonlinear predictor based on the Sugihara-May method [H. Gotoda, H. Nikimoto, T. Miyano, and S. Tachibana, Chaos 20, 013124 (2011); G. Sugihara and R. M. May, Nature 344, 734 (1990)] as well as a generalized radial basis function network as a global nonlinear predictor. The feasibility of a new approach based on short-term prediction is also discussed in this work from the practical viewpoint of combustion systems.

Dynamic properties of combustion instability in a lean premixed gas-turbine combustor

We experimentally investigate the dynamic behavior of the combustion instability in a lean premixed gas-turbine combustor from the viewpoint of nonlinear dynamics. A nonlinear time series analysis in combination with a surrogate data method clearly reveals that as the equivalence ratio increases, the dynamic behavior of the combustion instability undergoes a significant transition from stochastic fluctuation to periodic oscillation through low-dimensional chaotic oscillation. We also show that a nonlinear forecasting method is useful for predicting the short-term dynamic behavior of the combustion instability in a lean premixed gas-turbine combustor, which has not been addressed in the fields of combustion science and physics.

Investigation of short-range cedar pollen forecasting

Pollen forecasting is of increasing interest as a way to help the general public avoid contact with allergy-inducing pollen. It was recently reported that the dynamics underlying pollen concentration series is very similar to that of low-dimensional deterministic chaos, thus opening up new avenues of development in local pollen forecasting. Our analysis of hourly cedar pollen series for two seasons showed evidence of a small degree of determinism underlying the pollen time-series dynamics. However, we could not confirm that our pollen series was generated by a low-dimensional chaotic system. The nearest-neighbor method using local constant prediction applied to hourly pollen forecasting with a 1-h lead time was effective for small to medium pollen variations, but failed to reproduce large and intermittent pollen bursts. The performance of the nearest-neighbor model was significantly improved by applying a nonlinear filter to the source dataset. Standard time-series techniques such as neural networks did not improve upon these results. The difficulty in fully characterizing and accurately forecasting the pollen series was thought to originate in the nonstationarity of the series and in the large and intermittent pollen bursts that were found to have no apparent time structure. Thus the dynamics of hourly pollen series is probably not strongly tied to a low-dimensional chaotic system.

Detecting generalized synchrony: an improved approach

We examine some of the difficulties involved in detecting generalized synchrony (GS) in systems that exhibit noninvertibility and/or wrinkling. These latter features severely hinder identification of GS by conventional techniques. It is shown that it is possible to greatly improve detection by reducing the pseudofalse neighbors effects. Here we propose the delta(p)-neighbor method to overcome the noninvertibility effect and the delta(p,q) method to detect GS in systems with wrinkled structures.

Reconstructing embedding spaces of coupled dynamical systems from multivariate data

A method for reconstructing dimensions of subspaces for weakly coupled dynamical systems is offered. The tool is able to extrapolate the subspace dimensions from the zero coupling limit, where the division of dimensions as per the algorithm is exact. Implementation of the proposed technique to multivariate data demonstrates its effectiveness in disentangling subspace dimensionalities also in the case of emergent synchronized motions, for both numerical and experimental systems.