Bifurcations in Dynamical Systems

We considered the discrete map with quasi-periodic dynamics in the wide band of the parameters and investigated the structure of the parameter plane of two coupled maps. We revealed the doublings of 3D-tori, the systems of 2D-tori and synchronization tongues and the resonance web. Also we revealed the attractors with complex structure and the largest Lyapunov exponent close to zero.

Results of numerical investigation of bifurcations of one-parameter families of steady state regimes in a planar filtrational convection problem are presented. Galerkin’s method is applied for approximation of partial differential equations. As a result of the cosymmetry existence there are curves of equilibria with the hidden parameter. The algorithm of calculation of such curves is described. This algorithm can be applied to analyze systems with nonisolated sets of equilibria.