The attractors of two boundary value problems for a modifieded nonlinear telegraph equation

Two boundary value problems for a modified nonlinear telegraph equation are considered. The problem of invariant torus bifurcation has been studied for first of them. It is shown that only the torus of a larger dimension can be asymptotically stable and also that the dimension of this attractor increases as the main bifurcation parameter decreases. The latter means that Landau’s scenario of turbulence is realised in the problem under study. The existence of an infinitely dimensional attractor built up of unstable according to Lyapunov solutions has been shown for the second boundary value problem.