My Research

Estimating Parameter Spaces only from Time-Series data
(Reconstructing Bifurcation Diagram)

I estimate parameter spaces of unknown systems only from time-series data sets. In the estimated parameter space, bifurcation diagrams that are similar original bifurcation diagrams can be reconstructed. In addition, I analyze the estimated parameter space. In this research, parameter dimension and values are unknown, and time-series data sets generated by a system with different values are only used. Figure 1 shows an outline of this research.
In 1994, Tokunaga et al. proposed a method for reconstructing bifurcation diagrams [1]. By reconstructing the bifurcation diagrams, I can estimate oscillatory patterns when parameters are changed. In addition, if dynamics of the system can be analyzed, I expect that the system can be controlled and predicted.

Summary

Figure 1 : Outline of this research.


[1] Tokunaga et al., Reconstructing bifurcation diagrams only from time-waveforms, Physica D, No.79, 1994

What is the bifurcation diagram´╝č

Figure 2 shows the bifurcation diagram. I see changes of time-series data from this figure. Here, Figure 2 is the bifurcation diagram of an one-dimensional system. Therefore, horizontal and vertical axises are parameter and state values, respectively.

BifurcationDiagram

Figure 2 : Bifurcation diagrams.

What is the reconstruction of bifurcation diagrams´╝č

The bifurcation diagram is reconstructed only from time-series data. Here, the target system is unknown.

ReconstructingBifurcationDiagram

Figure 3 : Reconstruction of bifurcation diagrams.