Nonlinear Dynamics and Temporal Analysis

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Animal vocalizations range from tonal sounds produced by almost periodic vocal fold vibrations to completely aperiodic sounds generating noisy signals. Between these two extremes, a variety of nonlinear phenomena such as limit cycles, subharmonics, biphonation, chaos, and bifurcations have been found. This chapter introduces a concept of nonlinear dynamics and its methodology applicable to bioacoustic data. Since conventional spectral analysis is not sufficient to characterize nonlinear properties of the recorded sound signals, a temporal analysis based upon the method of nonlinear dynamics is developed. First, using a mathematical model of the vocal folds, basics of nonlinear dynamics and bifurcations are illustrated. The temporal analysis is then applied to acoustic data from real animal vocalizations. Our focus is on extracting low-dimensional nonlinear dynamics from several samples of vocalizations ranging from tonal sounds to irregular atonal sounds. We demonstrate that nonlinear analysis is a profitable approach for analyzing mammalian vocalizations with a harmonic composition or low-dimensional chaos.