Critical phenomena and bifurcations of solutions of infinite-dimensional systems of ordinary differential equations originating in some physical problems

We study critical phenomena and bifurcations of solutions of ordinary differential equations, having applications in some important and popular physical problems. We give the description of all spatially homogeneous solutions and find their bifurcations with respect to change of parameters. One studied a family of solutions, which are not spatially homogeneous, and their bifurcations with respect to change of initial data. One obtained the critical values of parameters and initial data such that by passing through which the qualitative behavior of solutions in the infinity change on principle.