Animal movement: symbolic dynamics and topological classification

Area of Science:

• Dynamical Systems
• Computational Biology
• Topology

Background:

• Classifying complex movements is challenging.
• Existing methods lack efficiency and simplicity.
• Understanding movement patterns is crucial in biology.

Purpose of the Study:

• To introduce a novel deterministic discrete dynamical system.
• To enable efficient simulation and classification of diverse movements.
• To apply topological methods for movement characterization.

Main Methods:

• Iterating a bimodal interval map.
• Utilizing symbolic dynamics and topological Markov chains.
• Topological classification of the dynamical system.

Main Results:

• Achieved efficient simulation capabilities.
• Developed a simple characterization for regular and complex motion.
• Demonstrated the system's applicability to animal movement.

Conclusions:

• The proposed dynamical system offers a powerful tool for movement analysis.
• Topological classification provides a robust framework for understanding motion.
• This method has significant potential for biological applications, particularly in animal movement studies.