In this work, a topological criterion is proposed for selecting a recurrence threshold for constructing a recurrence plot of a time series. It is based on a metric structure of the set of the recurrence plots that is defined by the recurrence plot deviation distance among recurrence plots, introduced in a previous paper by the authors. In this process for a range of threshold values, the corresponding recurrence plots are constructed. Then, a value of the threshold is considered to be optimal when the image of its recurrence plot remains close to images of the other recurrence plots constructed for close values of thresholds based on the topological criterion introduced in the present work. The results are applied both to time series emanating from the Lorenz dynamical system and to Molecular Dynamic simulations.

Non-recurrent congestion disrupts normal traffic operations and lowers travel time (TT) reliability, which leads to many negative consequences such as difficulties in trip planning, missed appointments, loss in productivity, and driver frustration. Traffic incidents are one of the six causes of non-recurrent congestion. Early and accurate detection helps reduce incident duration, but it remains a challenge due to the limitation of current sensor technologies. In this paper, we employ a recurrence-based technique, the Quadrant Scan, to analyse time series traffic volume data for incident detection. The data is recorded by multiple sensors along a section of urban highway. The results show that the proposed method can detect incidents better by integrating data from the multiple sensors in each direction, compared to using them individually. It can also distinguish non-recurrent traffic congestion caused by incidents from recurrent congestion. The results show that the Quadrant Scan is a promising algorithm for real-time traffic incident detection with a short delay. It could also be extended to other non-recurrent congestion types.

In the present paper, a topological classification of recurrence plots of time series that are constructed with equal embedding dimension and delay time is proposed by defining a metric structure in the set of those recurrence plots. To achieve this, the Recurrence Plot deviation distance and the Recurrence deviation plot are introduced along with qualitative and quantitative indices, which allows for a detailed comparison of the recurrence plots of two time series and their corresponding dynamical systems. In the range of values studied, the application of additive noise on the thermostat results in a less deterministic system behavior, quite close to that of the system with the unperturbed thermostat. On the other hand, multiplicative noise of small strength results in a less deterministic system quite close to the unperturbed system behavior. For a larger strength, the system presents a behavior which is significantly different from that of the unperturbed system. The new methodology introduced here provides detailed quantitative and graphical insights for the way that noise, additive and multiplicative, influences on the morphology of recurrence plots of the unperturbed and noise perturbed time series. The results are encouraging for potential future applications on the analysis of complex dynamical systems.

Understanding the underlying processes and extracting detailed characteristics of rivers is critical and has not yet been fully developed. The purpose of this study was to examine the performance of non-linear time series methods on environmental data. Specifically, we performed an analysis of water level measurements, extracted from sensors, located on specified stations along the Nestos River (Greece), with Recurrence Plots (RP) and Recurrence Quantification Analysis (RQA) methods. A more detailed inspection with the sliding windows (epoqs) method was applied on the Recurrence Rate, Average Diagonal Line and Trapping Time parameters, with results showing phase transitions providing useful information about the dynamics of the system. The suggested method seems to be promising for the detection of the dynamical transitions that can characterize distinct time windows of the time series and reveals information about the changes in state within the whole time series. The results will be useful for designing the energy policy investments of producers and also will be helpful for dam management assessment as well as government energy policy.

The visual boundary recurrence plot (VBRP) method is used in this analysis to study time series of fluctuating velocities in turbulent magnetohydrodynamic channel flow that were studied in our previous study using the theory of the recurrence plots. The VBRP is a new graphical tool, which visualizes each point of the recurrence plot with colors depending on whether the neighboring points are recurrent or not and enhances, thus, the study of the stability of the textures of the recurrence plots, viewing them as geometrical shapes. We calculate the VBRPs of the turbulent velocity time series of a simulated channel flow monitored at constant streamwise and spanwise positions and at a number of positions along the wall-normal direction. We further estimate the visual boundary recurrence plot rates to indicate the change of the dynamics of the flow. The results highlight the flow dynamics under the influence of the magnetic field and identify additional correlations/similarities between the flow point positions within the channel. In this study, we show that these areas correspond to perturbations due to strikes that are created close to the boundary and move toward the centerline. It also seems that we have more often creation of streaks in the case of absence of magnetic field.

In this paper, we compare the dynamics of the growth rates of the original Divisia monetary aggregates, the credit card-augmented Divisia monetary aggregates, and the credit card-augmented Divisia inside monetary aggregates. This analysis is based on the methods of recurrence plots, recurrence quantification analysis, and visual boundary recurrence plots which are phase space methods designed to depict the underlying dynamics of the system under study. We identify the events that affected Divisia money growth and point out the differences among the different Divisia monetary aggregates based on the recurrence and visual boundary recurrence plots. We argue that the broad Divisia monetary aggregates could be used for monetary policy and business cycle analysis as they are exhibiting less fluctuation compared to the narrow Divisia monetary aggregates. They could positively affect policy decisions regarding environmental choices and sustainability. We also point out the changes in the monetary dynamics locating the 2008 global financial crisis and the Covid-19 pandemic.