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MODA (Multiscale Oscillatory Dynamics Analysis) is a numerical toolbox developed by the
[Nonlinear & Biomedical Physics group](https://www.lancaster.ac.uk/physics/research/experimental-condensed-matter/nonlinear-and-biomedical-physics/) at [Lancaster University](https://www.lancaster.ac.uk/physics/) for analysing real-life time-series
that are assumed to be the output of some a priori unknown non-autonomous dynamical system,
that are assumed to be the output of some *a priori* unknown non-autonomous dynamical system,
and deriving important properties about this dynamical system from the time-series. It includes
methods both for analysing the recordings of a single signal over time, and for analysing a set
of recordings of multiple different signals over time. In particular, it has tools for analysing
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To use MODA, download the code and place it in a desired location. In your file explorer, double-click "MODA.m" inside the MODA folder to open it with MATLAB.

MODA can then be started using the "Run" button in the MATLAB editor.

## References

### Overview
1. J Newman, G Lancaster and A Stefanovska, “Multiscale Oscillatory Dynamics
Analysis”, v1.01, User Manual, 2018.
2. P Clemson, G Lancaster, A Stefanovska, “Reconstructing time-dependent dynamics”, *Proc IEEE*
**104**, 223–241 (2016).
3. P Clemson, A Stefanovska, “Discerning non-autonomous dynamics”, *Phys Rep* **542**, 297-368 (2014).

### Time-Frequency Analysis
1. D Iatsenko, P V E McClintock, A Stefanovska, “Linear and synchrosqueezed time-frequency
representations revisited: Overview, standards of use, resolution, reconstruction, concentration, and
algorithms”, *Dig Sig Proc* **42**, 1–26 (2015).
2. P Clemson, G Lancaster, A Stefanovska, “Reconstructing time-dependent dynamics”, *Proc IEEE*
**104**, 223–241 (2016).
3. G Lancaster, D Iatsenko, A Pidde, V Ticcinelli, A Stefanovska, “Surrogate data for hypothesis testing of
physical systems”, *Phys Rep* **748**, 1–60 (2018).

### Wavelet Phase Coherence
1. Bandrivskyy A, Bernjak A, McClintock P V E, Stefanovska A, “Wavelet phase coherence analysis:
Application to skin temperature and blood flow”, *Cardiovasc Engin* **4**, 89–93 (2004).
2. Sheppard L W, Stefanovska A, McClintock P V E, “Testing for time-localised coherence in bivariate
data”, *Phys. Rev. E* **85**, 046205 (2012).

### Ridge Extraction & Filtering
1. D Iatsenko, P V E McClintock, A Stefanovska, “Nonlinear mode decomposition: A noise-robust,
adaptive decomposition method”, *Phys Rev E* **92**, 032916 (2015).
2. D Iatsenko, P V E McClintock, A Stefanovska, “Extraction of instantaneous frequencies from ridges in
time-frequency representations of signals”, *Sig Process* **125**, 290–303 (2016).

### Wavelet Bispectrum Analysis
1. J Jamšek, A Stefanovska, P V E McClintock, “Wavelet bispectral analysis for the study of interactions
among oscillators whose basic frequencies are significantly time variable”, *Phys Rev E* **76**, 046221
(2007).
2. J Jamšek, M Paluš, A Stefanovska, “Detecting couplings between interacting oscillators with
time-varying basic frequencies: Instantaneous wavelet bispectrum and information theoretic approach”,
*Phys Rev E* **81**, 036207 (2010).
3. J Newman, A Pidde, A Stefanovska, “Defining the wavelet bispectrum”, submitted (2019).

### Dynamical Bayesian Inference
1. V N Smelyanskiy, D G Luchinsky, A Stefanovska, P V E McClintock, “Inference of a nonlinear stochastic model of the cardiorespiratory
interaction”, *Phys Rev Lett* **94**, 098101 (2005).
2. T Stankovski, A Duggento, P V E McClintock, A Stefanovska, “Inference of time-evolving coupled dynamical systems in the presence of noise”,
*Phys Rev Lett* **109**, 024101 (2012).
3. T Stankovski, A Duggento, P V E McClintock, A Stefanovska, “A tutorial on time-evolving dynamical Bayesian inference”, *Eur Phys J – Special
Topics* **223**, 2685-2703 (2014).
4. T Stankovski, T Pereira, P V E McClintock, A Stefanovska, “Coupling functions: Universal insights into dynamical interaction mechanisms”, *Rev
Mod Phys* **89**, 045001 (2017).
5. Special issue of the *Philos Trans Royal Soc A* (2019) with contributions by Kuramoto and others.

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