Animal movement: symbolic dynamics and topological classification

Carlos Ramos; Carlos Ramos

doi:10.3934/mbe.2019272

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 5: 5464-5489. doi: 10.3934/mbe.2019272

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Research article Special Issues

Animal movement: symbolic dynamics and topological classification

Carlos Ramos ^,

Department of Mathematics, Center of Mathematical Research and Applications, CIMA, University of Evora, Portuga

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.
- animal movement,
- iterated maps of the interval,
- symbolic dynamics,
- kneading sequences,
- topological entropy
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

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Abstract

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.

References

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