Schematic narrowband spectrograms illustrating stable limit cycle (a), frequency jump (b), subharmonics (c), biphonation (d) and deterministic chaos (E) (modified after Fig. 1 from Riede et al., 2004).
Spectrograms of representative right whale vocalizations exhibiting nonlinear phenomena (note: spectrograms are zoomed in on for better resolution). (a) Stable limit cycle (SLC). (b) SLC then initiation of subharmonics (SH) indicated by arrow. (c) SLC then a frequency jump (FJ) to a higher frequency. (d) Deterministic chaos (DC, initiation indicated by arrow) with an embedded nonparallel biphonation (BP), then a transition to a SLC. (e) SLC then BP in the form of sidebands (SB) being produced twice, the second time transitioning into DC.
Spectrograms of representative killer whale vocalizations exhibiting nonlinear phenomena (note: spectrograms are zoomed in on for better resolution). (a) Stable limit cycle (SLC) following the characteristic introductory buzz. (b) Introductory buzz then biphonation (BP) in the form of a nonparallel band and subharmonics (SH); is the high frequency component, is the low frequency component. (c) Nonparallel BP with sidebands (SB) appearing around the and a frequency jump (FJ) to a lower frequency with SB’s being produced at a new lower rate. (d) Introductory buzz followed by deterministic chaos (DC, initiation indicated by arrow) and then a transition into a nonparallel BP and a SLC.
Deterministic chaos analysis using the software program. (a) Spectrogram of a segment analyzed by the software program (rwc2 in Table II). This segment was cut from the vocalization seen in Fig. 2(e) at approximately and was the only segment which rejected the null hypothesis that the signal was a stationary, linear, random Gaussian signal. (b) Mutual information analysis to determine the appropriate time delay of each signal tested; taken as the first minimum (the noise segment was not further analyzed because its first minimum was ). Note: mutual information scale is logarithmic to better display results. Legend labels follow Table II. (c) False nearest neighbor analysis to determine the appropriate embedding dimensions; taken as point where the number of false neighbors decreases to zero. (d) The spectrum of Lyapunov exponents. All signals suspected of being chaotic exhibited one positive exponent indicating they are indeed non-Gaussian signals. Note: kwc1 had results at two iterations while all other segments had results at only one iteration; an iteration is a repetition process used by . Also, the exponent for the harmonic signal is the maximum exponent found; an additional exponent was found at .
Frequency of occurrence of nonlinear phenomena in the analyzed right whale (RW) and killer whale (KW) vocalizations: frequency jumps (FJ), subharmonics (SH), biphonation (BP), and deterministic chaos (DC).
Analysis of four signals exhibiting deterministic chaos and the generated harmonic and random signals.
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