The Differential-Delay Equations of Cancer Genetic Mechanisms
Results of qualitative analysis of the nonlinear functional-differential equations quantitatively describing activity of molecular-geneticВ system of an organism at norm and at a cancer are given (Hidirov, 1984, 2003). Qualitative research of the considered equations and their model systemsВ has shown presence trivial attractor (O), existence opportunity of unstable equilibria (A)and positive attractor (B) with infinite basin on theВ first quadrant of phase space. The positive attractor can lose own stabilityВ with the advent of auto-oscillations. Quantitative analysis (using PC at computation of parameter dynamicsВ for Lyapunov's number and Hausdorff's measure) has shown that the positive attractor can be transformed into a strange attractor.Then auto-oscillationsВ turn to irregular oscillatory decisions.Study of the parametrical portrait of model system for the functional-differential equations for molecular-geneticВ system of an organism has shown complex structure of chaos area and presence of failure area for oscillatory decisions in В trivial attractor basin (one ofВ the variants of "black hole" effect) (Hidirov, 2003). Study of genetic mechanisms of origin and developments of cancerous cells on the basis of the received results,В has shown the possibility and successfulness of hypothesises about existence in genome the ADS (Autonomous Development Systems), which operate the early embryonic development. ADS activation in somatic cells can bring to cancerВ origin.
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