Fig. 2. Spectral properties typical of three types of nonlinear phenomena; frequency jumps, subharmonics and deterministic chaos. (A) A 3500 Hz tone with two 250 Hz frequency jumps. A power spectrum (a) taken at arrow a shows a single peak of sound energy corresponding to f₀. (B) A 3750 Hz tone, with a series of bifurcations, the first from a single f₀ to a 0.5f₀ subharmonic regime, then an abrupt transition to deterministic chaos, and then to a 0.33f₀ subharmonic regime. Comparing spectra a and b illustrates the increase in spectral complexity resulting from the addition of subharmonic values and their harmonics (b in B). (C) A 10 ms section of deterministic chaos (in this case, a low-dimensional noise, generated using a Rossler attractor equation). The aperiodicity of the sound waveform (V) and the sound energy fairly evenly distributed across the entire spectrum (spectrogram C, and power spectrum, c) are indicators used to identify potential chaos in mockingbird songs. Abbreviations as in Tables 1 and 2; FJ, frequency jump; SH, subharmonics; CH, deterministic chaos; 1f₀, single frequency sounds; V, amplitude of sound waveform.