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Singing of Neoconocephalus robustus as an example of deterministic chaos in insects

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Abstract

We use nonlinear time series analysis methods to analyse the dynamics of the sound-producing apparatus of the katydid Neoconocephalus robustus. We capture the dynamics by analysing a recording of the singing activity. First, we reconstruct the phase space from the sound recording and test it against determinism and stationarity. After confirming determinism and stationarity, we show that the maximal Lyapunov exponent of the series is positive, which is a strong indicator for the chaotic behaviour of the system. We discuss that methods of nonlinear time series analysis can yield instructive insights and foster the understanding of acoustic communication among insects.

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References

  • Abarbanel H D I 1996 Analysis of observed chaotic data (New York: Springer)

    Google Scholar 

  • Behrman A 1999 Global and local dimensions of vocal dynamics; J. Acoust. Soc. Am. 105 432–443

    Article  PubMed  CAS  Google Scholar 

  • Fee M S, Shraiman B, Pesaran B and Mitra P P 1998 The role of nonlinear dynamics of the syrinx in the vocalizations of a songbird; Nature 395 67–71

    Article  PubMed  CAS  Google Scholar 

  • Fitch W T, Neubauer J and Herzel H 2002 Calls out of chaos: the adaptive significance of nonlinear phenomena in mammalian vocal communication; Anim. Behav. 63 407–418

    Article  Google Scholar 

  • Fletcher N H 2000 A class of chaotic bird calls?; J. Acoust. Soc. Am. 108 821–826

    Article  PubMed  CAS  Google Scholar 

  • Fraser A M and Swinney H L 1986 Independent coordinates for strange attractors from mutual information; Phys. Rev. A 33 1134–1140

    Article  PubMed  Google Scholar 

  • Hauser M D 1993 The evolution of nonhuman primate vocalizations: effects of phylogeny, body weight, and social context; Am. Nat. 142 528–542

    Article  Google Scholar 

  • Heath J E and Josephson R K 1970 Body temperature and singing in the katydid, Neoconocephalus robustus (Orthoptera, Tettigoniidae); Biol. Bull. 138 272–285

    Article  Google Scholar 

  • Hegger R and Kantz H 1999 Practical implementation of nonlinear time series methods: the TISEAN package; Chaos 9 413–440

    Article  PubMed  Google Scholar 

  • Hegger R, Kantz H and Schreiber T 1999 The official web page of the TISEAN project is: www.mpipks-dresden.mpg.de/:_tisean

  • Herzel H, Berry D, Titze I R and Saleh S 1994 Analysis of vocal disorders with methods from nonlinear dynamics; J. Speech Hear. Res. 37 1008–1019

    PubMed  CAS  Google Scholar 

  • Kantz H 1994 A robust method to estimate the maximal Lyapunov exponent of a time series; Phys. Lett. A 185 77–87

    Article  Google Scholar 

  • Kantz H and Schreiber T 1997 Nonlinear time series analysis (Cambridge: Cambridge University Press)

    Google Scholar 

  • Kaplan D T and Glass L 1992 Direct test for determinism in a time series; Phys. Rev. Lett. 68 427–430

    Article  PubMed  Google Scholar 

  • Kaplan D T and Glass L 1995 Understanding nonlinear dynamics (New York: Springer)

    Google Scholar 

  • Kennel M B, Brown R and Abarbanel H D I 1992 Determining embedding dimension for phase space reconstruction using a geometrical construction; Phys. Rev. A 45 3403–3411

    Article  PubMed  Google Scholar 

  • Kodba S, Perc M and Marhl M 2005 Detecting chaos from a time series; Eur. J. Phys. 26 205–215

    Article  Google Scholar 

  • Kumar A and Mullick S K 1996 Nonlinear dynamical analysis of speech; J. Acoust. Soc. Am. 100 615–629

    Article  Google Scholar 

  • Mende W, Herzel H and Wermke H 1990 Bifurcations and chaos in newborn infant cries; Phys. Lett. A 145 418–424

    Article  Google Scholar 

  • Narayanan S N and Alwan A A 1995 A nonlinear dynamical systems analysis of fricative consonants; J. Acoust. Soc. Am. 97 2511–2524

    Article  PubMed  CAS  Google Scholar 

  • Ott E 1993 Chaos in dynamical systems (Cambridge: Cambridge University Press)

    Google Scholar 

  • Perc M 2005a The dynamics of human gait; Eur. J. Phys. 26 525–534

    Article  Google Scholar 

  • Perc M 2005b Nonlinear time series analysis of the human electrocardiogram; Eur. J. Phys. 26 757–768

    Article  Google Scholar 

  • Riede T, Herzel H, Mehwald D, Seidner W, Trumler E, Tembrock G and Böhme G 2000 Nonlinear phenomena and their anatomical basis in the natural howling of a female dog-wolf breed; J. Acoust. Soc. Am. 108 1435–1442

    Article  PubMed  CAS  Google Scholar 

  • Riede T, Herzel H, Hammerschmidt K, Brunnberg L and Tembrock G 2001 The harmonic-to-noise-ratio applied to dog barks; J. Acoust. Soc. Am. 110 2191–2197

    Article  PubMed  CAS  Google Scholar 

  • Riede T, Mitchell B R, Tokuda I and Owren M J 2005 Characterizing noise in nonhuman vocalizations: acoustic analysis and human perception of barks by coyotes and dogs; J. Acoust. Soc. Am. 118 514–522

    Article  PubMed  Google Scholar 

  • Rosenstein M T, Collins J J and De Luca C J 1993 A practical method for calculating largest Lyapunov exponents from small data sets; Physica D 65 117–134

    Article  Google Scholar 

  • Salvino L W and Cawley R 1994 Smoothness implies determinism: a method to detect it in time series; Phys. Rev. Lett. 73 1091–1094

    Article  PubMed  Google Scholar 

  • Sauer T, Yorke J A and Casdagli M 1991 Embedology; J. Stat. Phys. 65 579–616

    Article  Google Scholar 

  • Schreiber T 1997 Detecting and analyzing nonstationarity in a time series with nonlinear cross-predictions; Phys. Rev. Lett. 78 843–846

    Article  CAS  Google Scholar 

  • Schuster H G 1989 Deterministic chaos (Weinheim: VCH)

    Google Scholar 

  • Scudder S H 1862 Materials for a monograph of the North American Orthoptera, including a catalogue of the known New England species; J. Boston Soc. Nat. Hist. 7 409–480

    Google Scholar 

  • Shaw R 1981 Strange attractors, chaotic behavior, and information flow; Z. Naturforsch. 36a 80–112

    Google Scholar 

  • Sprott J C 2003 Chaos and time-series analysis (Oxford: Oxford University Press)

    Google Scholar 

  • Strogatz S H 1994 Nonlinear dynamics and chaos (Massachusetts: Addison-Wesley)

    Google Scholar 

  • Takens F 1981 Detecting strange attractors in turbulence; in Lecture notes in mathematics (eds) D A Rand and L S Young (Berlin: Springer-Verlag) pp 366–381

    Google Scholar 

  • Titze I R, Baken R J and Herzel H 1993 Evidence of chaos in vocal fold vibration; in Vocal fold physiology: frontiers in basic science (ed) I R Titze (San Diego: Singular Publishing Group) pp 143–188

    Google Scholar 

  • Walker T J, Whitesell J J and Alexander R D 1973 The robust conehead: two widespread sibling species; Ohio J. Sci. 73 321–330

    Google Scholar 

  • Walker T J 1999 Web-version of handbook of crickets and katydids http://buzz.ifas.ufl.edu/

  • Wayland R, Bromley D, Pickett D and Passamante A 1993 Recognizing determinism in a time series; Phys. Rev. Lett. 70 580–582

    Article  PubMed  Google Scholar 

  • Wilden I, Herzel H, Peters G and Tembrock G 1998 Subharmonics, biphonation, and deterministic chaos in mammal vocalization; Bioacoustics 9 171–196

    Google Scholar 

  • Wolf A, Swift J B, Swinney H L and Vastano J A 1985 Determining Lyapunov exponents from a time series; Physica D 16 285–317

    Article  Google Scholar 

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Correspondence to Matjaž Perc.

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Benko, T.P., Perc, M. Singing of Neoconocephalus robustus as an example of deterministic chaos in insects. J Biosci 32, 797–804 (2007). https://doi.org/10.1007/s12038-007-0081-5

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