Various trajectories of design, arising from the new methodology of analog network design, are analyzed. Several major criteria suggested for optimal selection of initial approximation to the design process permit the minimization of computer time. The initial approximation point is selected with regard to the previously revealed effect of acceleration of the design process. The concept of separatrix is defined making it possible to determine the optimal position of the initial approximation. The numerical results obtained for passive and active networks prove the possibility of optimal choice of the initial point in design process.

We report relations between invariant manifolds of saddle orbits (Lyapunov family) around a saddle-center equilibrium point and lowest periodic orbits on the two degree of freedom swing equation system. The system consists of two generators operating onto an infinite bus. In this system, a stable equilibrium point represents the normal operation state, and to understand its basin structure is important in connection with practical situations. The Lyapunov families appear under conservative conditions and their invariant manifolds constitute separatrices between trapped and divergent motions. These separatrices continuously deform and become basin boundaries, if changing the system to dissipative one, so that to investigate those manifolds is meaningful. While, in the field of two degree of freedom motions, systems with saddle loops to a saddle-center are well studied, and existence of transverse homoclinic structure of separatrix manifolds is reported. However our investigating system has no such loops. It is interesting what separatrix structure exists without trivial saddle loops. In this report, we focus on above invariant manifolds and lowest periodic orbits which are foliated for the Hamiltonian level.