# Abstract:

A single-input homogeneous bilinear control system in $R^{3}$ is investigated to determine a class of bilinear control systems for which the feedback can lead to the chaotic behavior of the corresponding closed loop system. A simple and clearly formulated conjecture on the positive solution of the above problem is stated and investigated, both by analytical methods and by means of the computer simulation. It is shown that a rich class of bilinear systems with the chaotic behavior of the closed loop system exists, i. e. very simple by their form nonlinear systems can have very complicated behavior.

# Classification:

93C15, 93C10, 93D15, 58F13, 37D45, 34H05, 34C11