Mathematical modeling of probabilistic processes in neurodynamics: methods and algorithms of stochastic analysis in regular and chaotic zones

Project: Award Project


The project studied stochastic phenomena in nonlinear mathematical models describing neural activity. Two-dimensional FitzHugh-Nagumo and Morris-Lecar models, three-dimensional Hindmarsh-Rose model and four-dimensional Hodgkin-Huxley model were chosen for the research. Deterministic dynamics of these models differ in variety of types of bifurcations and behavioral regimes. In the stochastic variants of these models, a number of phenomena associated with effect of noise were discovered and studied. Among them are stochastic generation of multimodal oscillations, noise-induced transformation of spiking oscillations into bursting ones, noise-induced chaotization, and others. For a parametric analysis of the probabilistic mechanisms of these phenomena and the estimation of critical noise intensities, new universal methods of analysis were developed. The theoretical basis of the research is the original approach that use the stochastic sensitivity functions technique, the method of confidence domains and the technique of approximation of stochastic attractors of complex geometry. To implement the tasks of the project, specialized numerical procedures were built and software tools using modern computer technologies were developed.
Effective start/end date08/02/201631/12/2017


  • 27.35.43
  • RFFI
  • Kuibyshev Research Division