Local bifurcations in one version of the multiplier-accelerator model

The well-known mathematical model of macroeconomics “multiplier-accelerator” is considered in a nonlinear version with spatial factors. We study two versions of the corresponding boundary-value problem. In the first version, where the spatial dissipation is significant in the linear statement, the boundary-value problem has limit cycles that arise as a result of Andronov–Hopf bifurcations. The second version of the boundary-value problem arises when dissipation in the linear formulation is neglected. In this weakly dissipative version, the boundary-value problem has a countable set of finite-dimensional cycles and tori. All such invariant manifolds are unstable. The analysis of the problem is based on methods of the theory of infinite-dimensional dynamic systems.