A Predator-Prey Cellular Automaton with Parasitic Interactions and Environmental Effects

• Autorzy: Farina F. , Dennunzio A.
• Języki publikacji: EN

Abstrakty

EN

We propose a lattice model to describe a predator-prey system where two species with significantly different size are considered. The biological analogy we refer to is the predatory interaction between bacteria and viruses. We assume simple environmental effects altering the dynamics. Preys (bacteria) procreate by mitosis and they do not move. They may die because of natural causes or under the predation. The predation is the consequence of a diffusive phenomenon by the predators (viruses). Predators grow in number by infection and by prey self-immunity diseases, and they die by starvation.

Słowa kluczowe

EN

cellular automata; population dynamics; predator prey systems

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2008
• Tom: Vol. 83, nr 4
• Strony: 337--353
• Opis fizyczny: bibliogr. 21 poz., tab., wykr.

Twórcy

autor

Farina F.

autor

Dennunzio A.

• Dipartimento di Informatica, Sistemistica e Communicazione, Universita degli Studi di Milano-Bicocca, Via Bicocca degli Arcimboldi 8, 20126 Milano, Italy,

Bibliografia

• [1] Antal, T., Droz, M.: Phase transitions and oscillations in a lattice prey-predator model, Physical Review E, 63,2001,056-119(11).
• [2] Antal, T., Droz, M., Lipowski, A., Ódor, G.: Critical behaviour of a lattice prey-predator model, Physical Review E, 64, 2001,036-118(6).
• [3] Boccara, N., Roblin, O., Roger, M.: Automata network predator-prey model with pursuit and evasion, Physical Review E, 50, 1994,4531-4541.
• [4] Cattaneo, G., Dennunzio, A., Farina, F.: A Full Cellular Automaton to Simulate Predator-Prey Systems, Number 4173, in Lecture Notes in Computer Science, Springer, 2006, 446-451.
• [5] Droz, M., Pekalski, A.: Coexistence in a prey-predator system, Physical Review E, 63, 2001, 051-909(5).
• [6] Eden, M.: Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability (J. Ney-man, Ed.), University of California Press, Berkeley, 1961.
• [7] He, M., Ruan, H., Yu, C: A Predator-Prey Model Based on the Fully Parallel Cellular Automata, International Journal of Modern Physics C, 14, 2003, 1237-1249.
• [8] Hirsch, S.: Differential Equations, Dynamical Systems and Linear Algebra, Accademic Press, 1974.
• [9] Kovalik, M., Lipowski, A., Ferreira, A.: Oscillations and dynamics in a two-dimensional prey-predator system, Physical Review E, 66, 2002, 066-107(5).
• [10] Krieg, N., Holt, J., Bergey, D., Sneath, P.: Bergey's Manual of Determinative Bacteriology, 8aed., Williams &Wilkins, 1974.
• [11] van der Laan, J., Lhotka, L., Hogeweg, P.: Sequential Predation: a multi-model study, Journal of Theoretical Biology, 174, 1994, 149-167.
• [12] Lipowski, A.: Oscillatory behaviour in a lattice prey-predator system, Physical Review E, 60, 1999, 5179-5184.
• [13] Lotka, A.: Proc. Natl. Acad. Sci. U.S.A., 6, 1920, 410.
• [14] Murray, J.: Mathematical Biology, Springer Verlag, 1993.
• [15] Press, W., Teukolsky, S., Vetterling, W., Flannery, B.: Numerical Recipes in C: The Art of Scientific Computing, Cambridge University Press, 2002.
• [16] Ravasz, M., Szabó, G., Szolnoki, A.: Spreading of families in cyclic prey-predator models, Physical Review L,70,2004,012-901(4).
• [17] Reiter, C: A Local Cellular Model for Snow Crystal Growth, Chaos, Solitons & Fractals, 23, 2005, 1111- 1119.
• [18] Satulovsky, J., Tome, T.: Stochastic lattice gas model for a predator-prey system, Physical Review E, 49, 1994, 5073-5079.
• [19] Sherrat, J.: Periodic travelling waves in a family of deterministic cellular automata, Physica D, 95, 1996, 319-335.
• [20] Szabo, G., Sznaider, G.: Phase transition and selection in a four-species cyclic predator-prey model, Physical Review E, 69, 2004, 031-911(5).
• [21] Volterra, V.: Lesson sur la Theorie Matemathique de la Lutte pur la Vie, Gauthier-Villairs, 1931