| Popis: |
The work examines three nonlinear models proposed by Albert Goldbeter to describe the enzymatic reaction in a living cell. Mathematically, these nonlinear models are interesting for their slow-fast dynamics, canard-type self-oscillations, extreme inhomogeneity of deterministic phase portraits, great variability and coexistence of dynamic modes. Under these conditions, even small random perturbations significantly change the dynamics of the system and induce such phenomena as stochastic excitability, multimodality, phantom attractor, and transitions from order to chaos. The study of these models provides an understanding of the main mechanisms of these phenomena using methods of numerical and statistical analysis, as well as a theoretical approach based on the stochastic sensitivity function and the method of confidence domains. |
