@InProceedings{FreitasMaca:2016:PrCaSt,
               author = "Freitas, Celso Bernardo N{\'o}brega and Macau, Elbert Einstein 
                         Nehrer",
          affiliation = "{Instituto Nacional de Pesquisas Espaciais (INPE)} and {Instituto 
                         Nacional de Pesquisas Espaciais (INPE)}",
                title = "A preliminary case study about classic phase assignment 
                         techniques",
                 year = "2016",
         organization = "Workshop de Computa{\c{c}}{\~a}o Aplicada, 16. (WORCAP)",
             abstract = "Consensus quantification regarding experimental data often reveals 
                         valuable information for researches. For instance, solar 
                         irradiance exerts synchronization effects on Earths regional 
                         climate and the daily rhythm of cell division is controlled by the 
                         cells circadian clock. In the context of coupled oscillators, one 
                         may directly compute the norm of the differences between 
                         oscillators states over time. If after the transient these values 
                         become sufficiently small, it indicates a regime close to full 
                         synchronization, when oscillators converge to a common trajectory. 
                         On the other hand, several regimes commonly found in Nature can be 
                         characterized just via phase assignment. That is, one needs to 
                         specify coordinates along the limit cycle, with growth in the 
                         direction of the motion and 2Pi gain after each cycle. However, 
                         there seems to be no rigorous way to solve this problem for 
                         arbitrary chaotic systems. Thus, how do we compare phase 
                         assignment methods? For this purpose, we introduced in a previous 
                         work the Double Strip Test Bed (DSTB), which is a methodology to 
                         construct time series similar to the ones originated from chaotic 
                         oscillators. This approach relies on the well-known Kuramoto 
                         Model, and a transformation of its phase variables by embedding 
                         them into a three dimensional surface, in such a way to obtain 
                         curves with known phase variables a priori. We present here a 
                         numerical study regarding four methods commonly found in the 
                         literature: the classic Arctan method, the Arctan Method using the 
                         derivative of the time series, the Poincar{\'e} Surface Method 
                         and the Hilbert Transformation method. These techniques were 
                         applied to time series from two versions of the Rossler chaotic 
                         oscillator, coherent and non-coherent, and also from the DSTB. In 
                         the simplest case, the coherent one, all methods provided similar 
                         outcome. By analyzing the other scenarios, we point out advantages 
                         and limitations of each method.",
  conference-location = "S{\~a}o Jos{\'e} dos Campos, SP",
      conference-year = "25-26 out.",
           targetfile = "freitas_preliminary.pdf",
        urlaccessdate = "28 abr. 2024"
}