Delayed stochastic processes and animal movement interactions

• Main Author: McKetterick, Thomas John
• Published: University of Bristol 2015
• Subjects: 519
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.702110

Understanding delayed movement interactions has become an area of great interest and importance in the study of animal collective movement. This thesis investigates the role delays play in both theoretical and data-driven studies of movement interactions. From a data-set of bat paired flight trajectories empirical evidence is obtained for the delayed nature of the action and reaction between conspecifics. Analytic techniques are then developed for extracting the value of these delays and subsequently utilising this information to understand the sensory perception and leader-follower relationships of these animals. The combination of delays and noise present in animal movement interactions has not previously been incorporated in theoretical models due to a lack of exact analytic results for delayed stochastic processes. The second part of this thesis provides the theoretical foundations for studying linear delayed stochastic processes. A Langevin description of such systems is presented and from which an understanding of their delayed dynamics is obtained. The corresponding probability distribution is then calculated directly from the solution of the Langevin equation. An equivalent Fokker-Planck description is also derived and shown to provide a complete probabilistic understanding of these systems. Utilising these results, models of delayed movement interactions are presented and the role of delays in the resulting movement patterns is discussed. In the final part of this thesis, the Fokker-Planck description of these systems is used to investigate their evolution in the presence of boundaries.