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Multifractal random walk in copepod behavior

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  • Schmitt, Francccois G.
  • Seuront, Laurent

Abstract

A 3D copepod trajectory is recorded in the laboratory, using two digital cameras. The copepod undergoes a very structured type of trajectory, with successive moves displaying intermittent amplitudes. We perform a statistical analysis of this 3D trajectory using statistical tools developed in the field of turbulence and anomalous diffusion in natural sciences. We show that the walk belongs to “multifractal random walks”, characterized by a nonlinear moment scaling function for the distance versus time. To our knowledge, this is the first experimental study of multifractal anomalous diffusion in natural sciences. We then propose a new type of stochastic process reproducing these multifractal scaling properties. This can be directly used for stochastic numerical simulations, and is thus of important potential applications in the field of animal movement study, and more generally of anomalous diffusion studies.

Suggested Citation

  • Schmitt, Francccois G. & Seuront, Laurent, 2001. "Multifractal random walk in copepod behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 301(1), pages 375-396.
    • Handle: RePEc:eee:phsmap:v:301:y:2001:i:1:p:375-396
    DOI: 10.1016/S0378-4371(01)00429-0
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    References listed on IDEAS

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    1. Bacry, E. & Delour, J. & Muzy, J.F., 2001. "Modelling financial time series using multifractal random walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 84-92.
    2. Castiglione, P & Mazzino, A & Muratore-Ginanneschi, P, 2000. "Numerical study of strong anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 280(1), pages 60-68.
    3. Zaslavsky, George M, 2000. "Multifractional kinetics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 288(1), pages 431-443.
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    Cited by:

    1. Perisho, Shaun T. & Kelty-Stephen, Damian G. & Hajnal, Alen & Houser, Dorian & Kuczaj II, Stan A., 2016. "Fractal scaling in bottlenose dolphin (Tursiops truncatus) echolocation: A case study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 221-230.
    2. Seuront, Laurent & Spilmont, Nicolas, 2002. "Self-organized criticality in intertidal microphytobenthos patch patterns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 313(3), pages 513-539.
    3. Bao, Xiaomei & Tian, Canrong, 2019. "Delay driven vegetation patterns of a plankton system on a network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 74-88.
    4. Calif, Rudy & Schmitt, François G. & Huang, Yongxiang, 2013. "Multifractal description of wind power fluctuations using arbitrary order Hilbert spectral analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(18), pages 4106-4120.
    5. Kelty-Stephen, Damian G. & Mangalam, Madhur, 2024. "Additivity suppresses multifractal nonlinearity due to multiplicative cascade dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).

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