Research article Special Issues

Animal movement: symbolic dynamics and topological classification

  • Received: 15 January 2019 Accepted: 06 June 2019 Published: 13 June 2019
  • We present a deterministic discrete dynamical system, which is used to produce and classify a variety of types of movements. The dynamical system is determined by the iteration of a bimodal interval map, dependent on one real parameter, up to scaling. The characterization of the movements is based on the topological classification of the discrete dynamical system. Techniques from symbolic dynamics and topological Markov chains are used. With this approach we obtain efficient simulation capability and a very simple characterization of distinct types of regular or complex motion. We discuss the application of the method to describe animal movement.

    Citation: Carlos Ramos. Animal movement: symbolic dynamics and topological classification[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 5464-5489. doi: 10.3934/mbe.2019272

    Related Papers:

  • We present a deterministic discrete dynamical system, which is used to produce and classify a variety of types of movements. The dynamical system is determined by the iteration of a bimodal interval map, dependent on one real parameter, up to scaling. The characterization of the movements is based on the topological classification of the discrete dynamical system. Techniques from symbolic dynamics and topological Markov chains are used. With this approach we obtain efficient simulation capability and a very simple characterization of distinct types of regular or complex motion. We discuss the application of the method to describe animal movement.


    加载中


    [1] P. E. Smouse, S. Focardi, P. R. Moorcroft, et al., Stochastic modelling of animal movement, Phil. Trans. R. Soc. B, 365 (2010), 2201–2211.
    [2] R. Nathan, M. Getz, E. Revilla, et al., A movement ecology paradigm for unifying organismal movement research, Proc. Natl Acad. Sci. USA, 105 (2008), 19052–19059.
    [3] W. Tang and D. A. Bennett, Agent-based modeling of animal movement: a review, Geography Compass, 4 (2010), 682–700.
    [4] I. D. Jonsen, J. M. Flemming and R. A. Myers, Robust state–space modeling of animal movement data, Ecology, 86 (2005), 2874–2880.
    [5] T. A. Patterson, L. Thomas, C. Wilcox, et al., State–space models of individual animal movement, Trends Ecol. Evol., 23 (2008), 87–94.
    [6] B. T. McClintock, R. King, L. Thomas, et al., A general discrete-time modeling framework for animal movement using multistate random walks, Ecol. Monogr., 82 (2012), 335–349.
    [7] R. Langrock, R. King, J Matthiopoulos, et al., Flexible and practical modeling of animal telemetry data: hidden Markov models and extensions, Ecology, 93 (2012), 2336–2342.
    [8] S. Petrovskii, A. Mashanova and V. Jansen, Variation in individual walking behavior creates the impression of a Lévy flight, PNAS, 108 (2011), 8704–8707.
    [9] P. Tilles, S. Petrovskii and P. Natti, A random walk description of individual animal movement accounting for periods of rest, R. Soc. Open Sci., 3 (2016), 28018645.
    [10] J. P. Lampreia and J. Sousa Ramos, Symbolic dynamics of bimodal maps, Portugal. Math., 54 (1997), 1–18.
    [11] J. P. Lampreia, R. Severino and J. Sousa Ramos, Renormalizations for cubic maps, Ann. Math. Silesianae, 13 (1999), 257–270.
    [12] J. P. Lampreia, R. Severino and J Sousa Ramos, Irreducible complexity of iterated symmetrical bimodal maps, Discrete Dyn. Nat. Soc., 1 (2005), 69–85.
    [13] J. Milnor and C. Tresser, On entropy and monotonicity of real cubic maps, Stony Brook, IMS 1998/9 (1998), arXiv:math/9809096.
  • Reader Comments
  • © 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(3350) PDF downloads(558) Cited by(1)

Article outline

Figures and Tables

Figures(14)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog