Probabilistic lattice models of collective motion and aggregation: From individual to collective dynamics

Mathematical Biosciences

Volumn 156, Issue 1-2, 1999, Pages 255-269

  Deutsch, Andreas ^a   Lawniczak, Anna T ^b  

^a UNIVERSITY OF BONN   (Germany)

^b UNIVERSITY OF GUELPH   (Canada)

Author keywords

Aggregation; Cellular automaton model; Collective motion; Mean field assumption; Transport equation

Indexed keywords

AUTOMATION; CONFERENCE PAPER; MATHEMATICAL MODEL; MOTION; PATTERN RECOGNITION; POPULATION DYNAMICS; PROBABILITY; SIMULATION;

BIOLOGICAL TRANSPORT; CELL AGGREGATION; COMPUTER SIMULATION; MODELS, BIOLOGICAL;

EID: 0032896060     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0025-5564(98)10069-X     Document Type: Conference Paper

References (23)

1. D. Grünbaum, A. Okubo, Modelling social animal aggregations, manuscript.
2. K.P. Hadeler, Random walk systems modeling spread and interaction, CIME lectures at Martina Franca, June, 1997.
3. W. Alt, A. Deutsch, G. Dunn (Eds.), Dynamics of Cell and Tissue Motion, Birkhäuser, Basel, 1997.
4. B. Pfistner, A one-dimensional model for the swarming behaviour of myxobacteria, in: W. Alt, G. Hoffmann (Eds.), Biological Motion, Springer, Heidelberg, 1990, p. 556.
5. Pfistner B. Simulation of the dynamics of myxobacteria swarms based on a one-dimensional interaction model. J. Biol. Syst. 3(2):1995;579.
6. Steinberg M.S. Does differential adhesiveness govern self-assembly processes in histogenesis? Equilibrium configurations and emergence of a hierarchy among populations of embryonic cells. J. Exp. Zool. 173:1970;395.
7. S.R. Dunbar, H.G. Othmer, On a nonlinear hyperbolic equation describing transmission lines, cell movement, and branching random walks, in: H.G. Othmer (Ed.), Nonlinear Oscillations in Biology and Chemistry, Springer, Berlin, 1986, p. 274.
8. Othmer H.G., Dunbar S.R., Alt W. Models of dispersal in biological systems. J. Math. Biol. 26:1988;263.
9. Lawniczak A., Dab D., Kapral R., Boon J.P. Reactive lattice gas automata. Physica D. 47:1991;132.
10. Kapral R., Lawniczak A., Masiar P. Oscillations and waves in a reactive lattice-gas automaton. Phys. Rev. Lett. 66:1991;2539.
11. Kapral R., Lawniczak A., Masiar P. Reactive dynamics in a multi-species lattice-gas automaton. J. Chem. Phys. 96:1992;2762.
12. Boon J.P., Dab D., Kapral R., Lawniczak A. Lattice gas automata for reactive systems. Phys. Rep. 273(2):1996;55.
13. Deutsch A. Towards analyzing complex swarming patterns in biological systems with the help of lattice-gas cellular automata. J. Biol. Syst. 3:1995;947.
14. Deutsch A. Orientation-induced pattern formation: swarm dynamics in a lattice-gas automaton model. Int. J. Bifruc. Chaos. 6:1996;1735.
15. Bussemaker H.J. Analysis of a pattern-forming lattice-gas automaton: mean field theory and beyond. Phys. Rev. E. 53:1996;1644.
16. Bussemaker H., Deutsch A., Geigant E. Mean-field analysis of a dynamical phase transition in a cellular automaton model for collective motion. Phys. Rev. Lett. 78:1997;5018.
17. Edelstein-Keshet L., Ermentrout G. Models for contact-mediated pattern formation: cells that form parallel arrays. J. Math. Biol. 29:1990;33.
18. A. Deutsch, A. Lawniczak, Characterization of instabilities in lattice models of collective motion, manuscript in preparation.
19. C. Carcignani, The Boltzmann Equation and its Applications, Springer, Berlin, 1988.
20. A. Mogilner, A. Deutsch, J. Cook, Models for spatio-angular self-organization in cell biology, in: A. Deutsch, W. Alt, G.Dunn (Eds.), Dynamics of Cell and Tissue Motion, Ch. III.1, Birkhäuser, Basel, 1997, p. 173.
21. A. Deutsch, A new mechanism of aggregation in a lattice-gas cellular automaton model, Math. Comp. Mod. to appear.
22. T. Hillen, A Turing model with correlated random walk, Report No. 9 at Sonderforschungsbereich 382, Universities of Tübingen and Stuttgart, 1995.
23. A. Deutsch, M. Spielberg, L. Olsson, Cell-based modeling of salamander pigment pattern formation, manuscript in preparation.