Nonlinear time series analysis
Nonlinear time series analysis allows characterizing dynamical systems in which nonlinearity gives rise to a complex temporal evolution. Importantly, these nonlinear techniques can extract information from real-world experimental signals that cannot be resolved by classical linear techniques. While there is a long history of linear time series analysis, nonlinear methods have only just begun to reach maturity. Key targets of our work are the discrimination of deterministic and stochastic dynamics as well as the development of advance methods/algorithms for the classification and analysis of nonlinear response. These algorithms consist of the following exhaustive tools.
- Times Series Embedding and Reconstruction
- Dynamics measures and phase space topology
- Recurrence analysis and recurrence quantification
- Estimation of dynamic invariants (fractal dimensions, Lyapunov exponent)
- Ergodic theory
Applications are in the area of Nonlinear System Diagnostics, Machinery Dynamics, Biomedical diagnostics and systems control. Here are some specific projects.
- A novel integrated approach using nonlinear models and experimental data for system diagnostics
- Efficient and robust algorithm for complex nonlinear systems diagnostics
- Bifurcation analysis of time series based on advance time series analysis methods
- Estimation of dynamic invariants and measure for the prediction of Periventricular Leukomalacia
- A novel phase space topology method for complex system