Computer analysis of stochastic attractors for Goodwin's economical dynamics model
620083, Yekaterinburg, Lenina av., 51, Institute of Mathematics and Computer Science, Department of Mathematical Physics,1 pp. (accepted)
We study Goodwin’s economical dynamics model.
For the deterministic model, a full parametrical analysis of the attractors stability has been developed. From this investigation, the bifurcation diagram has been constructed. The phenomenon of the limit cycle generation when equilibria are still stable has been found and described. A behavior of the separatrix that divides basins of attraction of stable cycle and two stable equilibria has been studied in details.
Random trajectories of the stochastically forced model leave the deterministic attractor (equilibrium or cycle) and form corresponding stochastic attractor around it. The sensitivity of this stochastic attractor has been investigated by the stochastic sensitivity function technique. Using this method scattering regions of the attractor has been constructed. As noise intensity increases, a dispersion of random states increases too. But along with these quantitative changes a new qualitative deformation is observed. In this work we study phenomenon of generation of stochastic cycle in the parametrical zone where deterministic model has only stable equilibria.