Tatyana Ryazanova

Confidence Domains in the Analysis of Noise-Induced Transition to Chaos for Goodwin Model of Business Cycles

Stochastically forced Goodwin model of business cycles is considered. In a multistable zone, we study the phenomena of noise-induced transitions and chaotization. To clarify a probabilistic mechanism of these phenomena found numerically, we apply a semi-analytical method based on the stochastic sensitivity function technique and confidence domains. Using elaborated method, we estimate a critical value of the noise intensity corresponding to the onset of chaos.

Sensitivity analysis of consumption cycles

We study the special case of a nonlinear stochastic consumption model taking the form of a 2-dimensional, non-invertible map with an additive stochastic component. Applying the concept of the stochastic sensitivity function and the related technique of confidence domains, we establish the conditions under which the systems complex consumption attractor is likely to become observable. It is shown that the level of noise intensities beyond which the complex consumption attractor is likely to be observed depends on the weight given to past consumption in an individuals preference adjustment.

Analysis of Noise-Induced Bifurcations in the Stochastic Tritrophic Population System

A problem on the analysis of the noise-induced transitions in stochastically forced tritrophic population systems is considered. We study this problem on the basis of the conceptual “prey–predator-top predator” model which possesses coexisting attractors (limit cycles) and exhibits noise-induced transitions between them. For the parametric analysis of noise-induced phenomena in this nonlinear 3D model, we suggest a constructive approach combining the stochastic sensitivity function technique and confidence domain method. We show how increasing noise causes stochastic bifurcations, generation of mixed-mode oscillations, and transitions from order to chaos.

EXCITABILITY AND COMPLEX MIXED-MODE OSCILLATIONS IN STOCHASTIC BUSINESS CYCLE MODEL

Stochastically forced business cycle model is considered. We study a phenomenon of the noise-induced generation of complex mixed-mode oscillations in zones where the deterministic model exhibits a single attractor (equilibrium or limit cycle). A probabilistic mechanism of the transition from unimodal oscillations to the intermittency of small- and large-amplitude stochastic oscillations is investigated on the base of the stochastic sensitivity functions technique. We show that such intermittency, connected with the nonuniformity of phase portrait, can be parametrically analyzed by the confidence domains method.