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Dynamical and computational structures under the sea: hybrid modelling of fish motion

• Background:
  
  Nature is a never ending source of inspiration for Science; and for Engineering, as well. The pursuit of models for describing the collective behaviour of animals or insects can be very useful for solving specific problems encountered in some emerging engineering applications. This is the case of the motion of an ant colony, a school of fish or a flock of birds, which are used as a reference in a wide range of applications, such as, cooperative robotics, computer animation, multi-agent control design, distributed computer systems, or social networks modelling.
  
  School of fish are an interesting example of synchronised bio-group dynamics and collective behaviour. Different models have been proposed to study how the fish motion evolve dynamically and how they change their structure in order to forage, to survive under unfavorable conditions or simply to migrate. Two key ideas have to be considered ir order to obtain a model for fish collective and self-organised behaviour: 1) individual fish following elementary behavioural rules can produce complex behavioural patterns, 2) individual fish achieve a global goal with minimal communication with other fish in the school, and without having a complete picture of their position in the overall structure, they have only information of their closest neighbours. This type of behaviour implies different discrete transitions and the interaction of different types of dynamics (discrete and continuous). That is, the motion of a school of fish could be considered as an example of hybrid dynamical system, and can be described by means of a hybrid automaton [3].
  


• Description:
  
  This project has two main goals. First, to propose a hybrid dynamical model for the collective behaviour of a school of fish. The model to propose will be inspired in previously proposed models of flocking [1,3,4,5,7,8]. Second, to simulate the model and produce graphical visualitations of the results.


• Deliverables:
  
  
  • A hybrid dynamical model to describe the group behaviour of a school of fish.
  • Programs to simulate the model proposed.
  • A study of the dynamical patterns identified in the simulations.
  • Graphical visualisations of the dynamical behaviours.


• Supervisor: Dr. Eva Navarro López.


• Suitability:
  
  Students keen on exploring inter-disciplinary work are invited to this project. Enthusiasm for dynamical systems theory and simulation, programming, graph and automata theory is also desirable.


• Some references:
  
  [1] I.D. Couzin, J. Krause, N.R. Franks, S.A. Levin, 'Effective leadership and decision-making in animal groups on the move', Nature, vol. 433(3), 513-516, 2005.
  
  [2] I.D. Couzin, J. Krause, R. James, G.D. Ruxton, N.R. Franks, 'Collective memory and spatial sorting in animal groups', Journal of Theoretical Biology, vol. 218, 1-11, 2002.
  
  [3] T.A. Henzinger. "The theory of hybrid automata". Proc. 11th IEEE Symposium of Logic in Computer Science, pp. 278-292, 1996.
  
  [4] S. Martínez, J. Cortés, F. Bullo, 'Motion coordination with distributed information', IEEE Control Systems Magazine, vol. 27(4), 75-88, 2007.
  
  [5] C.W. Reynolds, 'Flocks, herds and schools: a distributed behavioural model', Computer Grapics, vol. 21, 25-33, 1987.
  
  [6] D.J.T. Sumper, 'The principles of collective animal behaviour', Philosophical Transactions of the Royal Society B, vol. 361, 5-22, 2006.
  
  [7] T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen, O. Shochet, 'Novel type of phase transition in a system of self-driven particles', Physical Review Letters, vol. 75(6), pp. 1226-1229, 1995.
  
  [8] A. J. Wood, G. J. Ackland, 'Evolving the selfish herd: Emergence of distinct aggregating strategies in an individual-based model', Proceedings of the Royal Society, vol. 274, pp. 1637–1642, 2007.