Structure of the Jacobian in economic growth models*

The paper deals with the Hamiltonian systems arising in optimal control problems for economic growth models. Qualitative analysis of the Hamiltonian dynamics plays a significant role for investigating the asymptotic behavior of optimal trajectories in the case of the existence of steady states. In the framework of this analysis, numerical algorithms are elaborated for constructing optimal solutions in economic growth models relied on the stabilization technique. This approach supposes that the steady state exists and has the saddle character. The recent research of authors allows to extend these methods for the circle character of the steady state. In this case, the natural question arises concerning criteria of the existence of the non-linear stabilizer for the Hamiltonian system. Basing on properties of the Hamiltonian matrices one can provide the analysis of the steady state character and investigate its sensitivity with respect to model parameters. The paper deals with examination of properties of the Hamiltonian systems and the sensitivity analysis of optimal model trajectories. It contains proofs of related theoretical results and demonstrates examples by applying the proposed technique to one-factor and two-factor growth models.