Synthesis of Radiating Systems with Flat Aperture According to a Given Power Directivity Pattern. ІІ. Finding Solutions at the Bifurcation Points

Abstract

We continue our investigation of the problem of synthesis for a radiating system with flat aperture according to a prescribed power directivity pattern originated in [P. O. Savenko, J. Math. Sci.,208, No. 3, 366–381 (2015)]. As a characteristic feature of problems from this class, we can mention the non-uniqueness and bifurcations of their solutions. On the basis of the theory of branching, we present a technique of finding the nonzero solutions (in the first approximation). This technique enables us to determine the main properties of solutions, which significantly simplifies the problem of finding the optimal solutions of the problem of synthesis by numerical methods.