Related Experiment Video
Updated: Oct 1, 2026

Assessing Cerebral Autoregulation via Oscillatory Lower Body Negative Pressure and Projection Pursuit Regression
Published on: December 10, 2014
Reconstructing bifurcation diagrams from noisy time series using nonlinear autoregressive models
E Bagarinao1, K Pakdaman, T Nomura
1Division of Biophysical Engineering, Department of Systems and Human Science, Graduate School of Engineering Science, Osaka University, Toyonaka City, Osaka 560-8531, Japan.
Abstract:
We introduce a formalism for the reconstruction of bifurcation diagrams from noisy time series. The method consists in finding a parametrized predictor function whose bifurcation structure is similar to that of the given system. The reconstruction algorithm is composed of two stages: model selection and bifurcation parameter identification. In the first stage, an appropriate model that best represents all the given time series is selected. A nonlinear autoregressive model with polynomial terms is employed in this study. The identification of the bifurcation parameters from among the many model parameters is done in the second stage. The algorithm works well even for a limited number of time series.
Related Concept Videos
Linear Approximation in Frequency Domain
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Reconstruction of Signal using Interpolation
Modeling with Differential Equations
BIBO stability of continuous and discrete -time systems
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Linear time-invariant Systems
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be calculated...