Non-linear dynamic systems, pattern formation and self-organization in biological
and chemical systems
The main results
concern general problems of dissipative structure models, such as existence and
stability of solutions, spatial mode selection, reduction of models and also
mathematical models of specific biological and chemical systems demonstrating
stationary pattern formation. Namely the models, explaining spatial patterning by
bacterial colonies, Liesegang precipitation patterns, periodic patterning in
vertebrates and light-triggered electro-chemical patterns on membranes of
Charasean cells were suggested
the main direction of research is investigation of Turing and non-Turing
mechanisms of pattern formation; modelling of self-organization in biological and
chemical systems including chemotactic cell aggregation, tumour growth,
electro-chemical patterns on a cellular level and precipitation patterns
List of selected publications:
1. A.A.Polezhaev, S.C.Muller. Complexity of precipitation patterns: Comparison of simulation with experiment. Chaos, 1994, v.4(4), p.631-636.
2. A.A.Polezhaev. Phase waves in oscillatory media. Physica D, 1995, v.84, p.253-259.
3. A.A.Polezhaev. Mathematical modelling of the mechanism of vertebrate somitic segmentation. J.Biol.Syst., 1995, v.3(4), p.1041-1051.
4. A.B.Goryachev, A.A.Polezhaev, D.S.Chernavskii. Catastrophic extinction, noise-stabilized turbulence and unpredictability of competition in a modified Volterra-Lotka model. Chaos, 1996, v.6(1), p78-86.
5. A.A.Polezhaev, V.S.Zykov, S.C.Muller. Destabilization of cell aggregation under nonstationary conditions. Phys.Rev.E, 1998, v.58(5), p.6328-6332.
6. A.A.Polezhaev. Mathematical modelling of somite segmentation in vertebrates. In: Origin and Fate of Somites (ed. by E.J.Sanders, J.W.Lash and C.P.Ordahl), IOS Press: Amsterdam, 2001, p. 107-115.
7. A.V.Kolobov, A.A.Polezhaev, G.I.Solyanik. The role of cell motility in metastatic cell dominance phenomenon: analysis by a mathematical model. J.Theor.Med., 2001, v.3, p.63-77.
8. A.A.Bulychev, A.A.Polezhaev, S.V.Zykov, T.Yu.Pljusnina, G.Yu.Riznichenko, A.B.Rubin, W.Jantoss, V.S.Zykov, S.C.Muller. Light-triggered pH Banding Profile in Chara Cells Revealed with a Scanning pH Microprobe and its Relation to Self-Organization Phenomena. J.Theor.Biol., 2001, v.212, 275-294.