Mathematical Modelling of the Micromicetes Colonies Growth Applying the Diffusion Equation

ABSTRACT

We have studied the mathematical model of
the growth of a micromycetes colony. The results of the numerical experiments have shown that the model given in
the work quite adequately reflects the emergence of the ring structures in the
micromycetes colonies.

Cite this paper

A. Idiyatullina, L. Vodopyanova and V. Vodopyanov, "Mathematical Modelling of the Micromicetes Colonies Growth Applying the Diffusion Equation,"*Advances in Microbiology*, Vol. 3 No. 8, 2013, pp. 7-10. doi: 10.4236/aim.2013.38A002.

A. Idiyatullina, L. Vodopyanova and V. Vodopyanov, "Mathematical Modelling of the Micromicetes Colonies Growth Applying the Diffusion Equation,"

References

[1] A. N. Kolmogorov, I. G. Petrovsky and N. S. Piskunov, “Research of the Equation of the Diffusion Connected to Increase of Quantity of Substance, and Its Application to One Biological Problem,” Bulletin of the Moscow State University, Vol. 1, No. 6. 1937, pp. 1-26.

[2] J. Adler, “Chemotaxis in Bacteria,” Science, Vol. 153, No. 3737, 1966, pp. 708-716.

http://dx.doi.org/10.1126/science.153.3737.708

[3] E. F. Keller and L. A. Segel, “Model for Chemotaxis,” Journal of Theoretical Biology, Vol. 30, No. 2, 1971, pp. 225-234.

http://dx.doi.org/10.1016/0022-5193(71)90050-6

[4] A. A. Polezhaev and M. O. Ptitsyn, “The Mechanism of Emergence of Existential Orderliness in Bacterial Systems,” Biophysics, Vol. 35, No. 2, 1990, pp. 302-306.

[5] A. L. Bulyanitsa, E. V. Bogomolova, E. Yu. Bystrov, V. E. Kurochkin and L. K. Panin, “Model of Formation of Ring Structures in Colonies of Mitselialny Fungi,” The Magazine of the General Biology, Vol. 61, No. 4, 2000, pp. 400-411.

[6] A. L. Bulyanitsa and V. E. Kurochkin, “Research of Processes of Ordering in Open Systems (on the Example of Evolution of a Colony of Imperfect Mitselialny Fungi),” Scientific Instrument Making, Vol. 10, No. 2, 2000, pp. 43-49.

[7] A. L. Bulyanitsa, E. Yu. Bystrov, V. E. Kurochkin, L. K. Panin and E. V. Bogomolova, “Influence of Coefficient of Diffusion of Metabolites on Ordering Processes in Colonies of Imperfect Mitselialny Fungi,” Scientific Instrument Making, Vol. 10, No. 4, 2000, pp. 44-47.

[8] E. O. Tsvetkova, A. L. Bulyanitsa, V. E. Kurochkin, L. K. Panin and E. V. Bogomolova, “Influence of Adaptation Ability on Casting Processes in Colonies of Mitselialny Fungi,” Scientific Instrument Making, Vol. 11, No. 4, 2001, pp. 76-79.

[9] A. L. Bulyanitsa, “Phase Transitions in Colonies of Imperfect Mitselialny Fungi,” Scientific Instrument Making, 2004, Vol. 14, No. 3, pp. 97-101.

[1] A. N. Kolmogorov, I. G. Petrovsky and N. S. Piskunov, “Research of the Equation of the Diffusion Connected to Increase of Quantity of Substance, and Its Application to One Biological Problem,” Bulletin of the Moscow State University, Vol. 1, No. 6. 1937, pp. 1-26.

[2] J. Adler, “Chemotaxis in Bacteria,” Science, Vol. 153, No. 3737, 1966, pp. 708-716.

http://dx.doi.org/10.1126/science.153.3737.708

[3] E. F. Keller and L. A. Segel, “Model for Chemotaxis,” Journal of Theoretical Biology, Vol. 30, No. 2, 1971, pp. 225-234.

http://dx.doi.org/10.1016/0022-5193(71)90050-6

[4] A. A. Polezhaev and M. O. Ptitsyn, “The Mechanism of Emergence of Existential Orderliness in Bacterial Systems,” Biophysics, Vol. 35, No. 2, 1990, pp. 302-306.

[5] A. L. Bulyanitsa, E. V. Bogomolova, E. Yu. Bystrov, V. E. Kurochkin and L. K. Panin, “Model of Formation of Ring Structures in Colonies of Mitselialny Fungi,” The Magazine of the General Biology, Vol. 61, No. 4, 2000, pp. 400-411.

[6] A. L. Bulyanitsa and V. E. Kurochkin, “Research of Processes of Ordering in Open Systems (on the Example of Evolution of a Colony of Imperfect Mitselialny Fungi),” Scientific Instrument Making, Vol. 10, No. 2, 2000, pp. 43-49.

[7] A. L. Bulyanitsa, E. Yu. Bystrov, V. E. Kurochkin, L. K. Panin and E. V. Bogomolova, “Influence of Coefficient of Diffusion of Metabolites on Ordering Processes in Colonies of Imperfect Mitselialny Fungi,” Scientific Instrument Making, Vol. 10, No. 4, 2000, pp. 44-47.

[8] E. O. Tsvetkova, A. L. Bulyanitsa, V. E. Kurochkin, L. K. Panin and E. V. Bogomolova, “Influence of Adaptation Ability on Casting Processes in Colonies of Mitselialny Fungi,” Scientific Instrument Making, Vol. 11, No. 4, 2001, pp. 76-79.

[9] A. L. Bulyanitsa, “Phase Transitions in Colonies of Imperfect Mitselialny Fungi,” Scientific Instrument Making, 2004, Vol. 14, No. 3, pp. 97-101.