Advertisement

Cell Automata Models for a Reaction-Diffusion System

  • Costin-Radu Boldea
  • Afrodita Balasa Boldea
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 27)

Abstract

This paper presents two ultra-discrete versions (discrete time, space, and values) of an important reaction-diffusion system arising from the biomathematical domain, the so-called predator-prey interaction system.

Keywords

Cellular Automaton Cellular Automaton Cellular Automaton Model Cellular Automaton Model Diffusion Part 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Boldea CR A hierarchy for the completely integrable RDS system. Tensor N S 66(3):260–267Google Scholar
  2. 2.
    Garvie MR (2006) Finite-difference schemes for reaction-diffusion equations modeling predator-prey interactions in MATLAB. Bull Math Biol 69(3):931–956CrossRefMathSciNetGoogle Scholar
  3. 3.
    Joshi N, Ormerod C (2007) The general theory of linear difference equations over the max-plus semi-ring. Stud Appl Math 118(1):85–97(13)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Kang H, Pesin Y (2005) Dynamics of a discrete Brusselator model: escape to infinity and Julia set. Milan J Math 73:1–17CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Martina I, Pashaev OK, Soliani G (1998) Phys Rev D 58 084025Google Scholar
  6. 6.
    Murray JD (1989) Mathematical biology. Springer-Verlag, New YorkMATHGoogle Scholar
  7. 7.
    Ramani A, Takahashi D, Grammaticos B, Ohta Y (1998) The ultimate discretisation of the Painlevé equations. Physica D 114:185–196CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Takahashi D, Satsuma J (1990) A soliton cellular automaton. J Phys Soc Japan 59:3514–3519CrossRefMathSciNetGoogle Scholar
  9. 9.
    Tokihiro T, Takahashi D, Matsukidaira J, Satsuma J (1996) From soliton equations to integrable cellular automata through a limiting procedure. Phys Rev Lett 76:3247–3250CrossRefGoogle Scholar
  10. 10.
    Wolfram S (2003) New constructions in cellular automata. In: Proceedings of the Conference, Santa Fe, NM, 1998. Oxford University Press, New YorkGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of Computer ScienceWest University of TimisoaraTimisoara 1900Romania

Personalised recommendations