Power Regulation in a Group of Radio Stations

A descriptive investigation is made of a group of radio stations creating mutual interference. The study of the possible modes of operation of the radio stations of the group leads to the consideration of a matrix with positive diagonal and negative nondiagonal elements. It is shown that the vector of the attainable noise/signal ratios must belong to a certain infinitely connected $\Lambda^n$-domain which is not identical with the positive orthant of the corresponding space. Local stability of power regulation is established, this being a necessary condition for the stability of the choice of some (attainable) vector of the noise/signal ratios by means of an independent power regulation carried out by each transmitter.