Experimental studies of chaotic dynamics near the Theorist

Abstract

The purpose of this work is to review of works in which experimental studies of the regularities of chaotic dynamics revealed theoretically in works of S.P. Kuznetsov were carried out. Methods. The research methods used are primarily based on the construction of experimental schemes; they correspond most closely to the mathematical models proposed and theoretically and numerically investigated by S.P. Kuznetsov. These are systems of radio engineering oscillators with various types of communication and impact, autogenerators with various types of feedback. Results. The transition to chaos in the electron beam – backward electromagnetic wave system is investigated using the example of a backward wave tube. On the example of coupled nonlinear radio engineering oscillators with in-phase excitation, the discovered S.P. Kuznetsov, universal regularities and similarity laws for coupled systems with period doubling. The paper presents results of experimental study of radiophysical devices, on the example of which it was possible to verify the universal laws of the critical behavior of two unidirectionally coupled systems with period doublings. The results of joint with S.P. Kuznetsov of experimental studies, which for the first time in the world presented convincing arguments for the existence of a transition to chaos through the birth of a strange non-chaotic attractor. An experimental system with delayed feedback is presented for theoretical regularities testing that appear on the threshold of the transition to chaos. The experimentally developed by S.P. Kuznetsov’s scheme of an auto-generator of hyperbolic chaos, which, apparently, is the world’s first known example of a physical system with rough chaos.

Keywords

• universality
• scaling
• critical behavior
• period doubling
• quasi-periodicity
• strange non-chaotic attractor
• hyperbolic chaos