Reconstructing bifurcation diagrams of dynamical systems using measured time series

Area of Science:

• Dynamical Systems and Chaos Theory
• Computational Neuroscience
• Time Series Analysis

Background:

• Reconstructing bifurcation structures from time series data is crucial for understanding complex dynamical systems.
• Existing methods often struggle with noise and multiparameter optimization.
• Accurate reconstruction of bifurcation diagrams (BDs) is essential for characterizing system dynamics.

Purpose of the Study:

• To develop a robust algorithm for reconstructing the bifurcation structure of dynamical systems from time series data.
• To apply the algorithm to a neuron model for validating its effectiveness.
• To demonstrate the algorithm's ability to capture complex system behaviors and its robustness to noise.

Main Methods:

• Utilizing nonlinear autoregressive (NAR) models with polynomial terms as parameterized predictor functions.
• Employing a fast orthogonal search scheme to efficiently select appropriate NAR model terms.
• Applying the algorithm to simulated membrane potential waveforms from a neuron model.

Main Results:

• The algorithm successfully reconstructed the bifurcation diagram (BD) of the neuron model.
• The reconstructed BD accurately reflected the different dynamical behaviors of the original system.
• The method demonstrated robustness to noise and effectiveness with limited time series data.

Conclusions:

• The presented algorithm provides an effective and robust method for reconstructing bifurcation structures from time series.
• This approach facilitates the analysis of complex dynamical systems, including neural models.
• The algorithm's performance with limited data opens new avenues for experimental time series analysis.