Exploring nonlinearity by feedback

The possibilities of studying nonlinear behavior of physical systems by small feedback action are discussed. Analytical bounds of possible system energy change by feedback are established. It is shown that for a 1-DOF nonlinear oscillator, the change of energy by feedback can reach the limit achievable for a linear oscillator by a harmonic (non-feedback) action. The results are applied to different physical problems: evaluating the amplitude of action leading to escape from a potential well; stabilizing unstable modes of a nonlinear oscillator (pendulum); using feedback testing signals in spectroscopy. These and related studies are united by similarity of their goals (examination possibilities and limitations for changing a system behavior by feedback) and by unified methodology borrowed from cybernetics (control science). They, therefore, constitute a part of physics which can be called cybernetical physics. (C) 1999 Elsevier Science B.V. All rights reserved.