Anishchenko-Astakhov self-sustained oscillator as one of the basic models of deterministic chaos

In the present review the conditions of appearing chaotic self-sustained oscillations are formulated and a radio-technical scheme of a generator realizing these conditions is given. The equations of Anishchenko-Astakhov's generator are derived and analyzed. A special attention is paid to the interrelation between the generator's equations and Theodorchik and Van der Pole classical models. We justify a fundamental reason of the onset of chaotic self-sustained oscillations, that is related with the presence of a homoclinic trajectory in the form of a saddle-focus separatrix loop. We briefly describe the major research results that have firstly been obtained numerically and experimentally by using Anishchenko-Astakhov's generator.