Investigating Possible Deterministic Chaos in Syllables of Zebra Finch Song
Open Access
- Author:
- Vidmar, David Michael
- Area of Honors:
- Physics
- Degree:
- Bachelor of Science
- Document Type:
- Thesis
- Thesis Supervisors:
- Dezhe Jin, Thesis Supervisor
Dr. Richard Wallace Robinett, Thesis Honors Advisor - Keywords:
- chaos
zebra finch
time series analysis
nonlinear dynamics
songbird vocalization
maximal lyapunov exponents
minimum embedding dimension - Abstract:
- A proposed model for Zebra finch song production, based upon a modified Van der Pol oscillator, is detailed. By adding a time-dependence to the parameters in this model, syllables are simulated and compared to their real-world counterparts. These simulated syllables are shown to accurately recreate various observed real-world syllables. The complexity of birdsong waveforms and spectrograms is also examined, and the possibility of deterministic chaos being the cause for such complexity is proposed. Attempts to add this chaos into the model by way of tweaking parameters is shown to be unsuccessful, due to the sensitivity of this system's chaotic regime to changing parameters. The question of chaotic syllables, however, still remains, and predictive algorithms are outlined to determine properties of the governing system of any experimentally determined time series. In the case of birdsong, the time series is that of pressure amplitude, and these methods are used to investigate the fundamental nature of the governing dynamics of song production. By analyzing whole syllables, first, two cases of predicted chaos are discovered, shown as positive maximal Lyapunov exponents on the order of .005. Taking the analysis of only a small window, and scanning this window of analysis across the whole data, a time dependent Lyapunov function is calculated and plotted over the song waveform. This is shown to have spikes at certain common syllables, which are implied to be slightly chaotic. The calculation of these exponents is shown to depend greatly on a user-defined parameter, and questions about its validity are raised. Namely, it is shown that these established methods imply chaos for systems which are known to be non-chaotic. It seems that the culprit is the time-varying parameters, which can throw off these methods in even the simplest systems. Because of this flaw in the algorithms, these results, as well as previously published results about chaos in animal vocalizations, seem inconclusive at best. Further analysis remains to be done to determine if any chaos exists in these systems, or if the time-varying parameters known to be present in such systems are the only reason that these algorithms imply chaos.