Hidden attractors in Chua circuit: mathematical theory meets physical experiments

Abstract After the discovery in early 1960s by E. Lorenz and Y. Ueda of first example a chaotic attractor numerical simulation real physical process, new scientific direction analysis behavior dynamical systems arose. Despite key role this discovery, later on number works have appeared supposing that attractors considered models are rather artificial, computer-induced objects, i.e., they generated not due to nature but only errors arising from application approximate methods finite-precision computations. Further justification for possibility existence chaos study system developed two directions. Within direction, effective analytic-numerical were invented providing so-called computer-assisted proof attractor. In framework second attempts made detect directly experiment, designing proper experimental setup. The remarkable result is experiment L. Chua, which he designed simple RLC circuit (Chua circuit) containing nonlinear element diode), managed demonstrate evidence screen oscilloscope. mathematical model Chua (further, system) also known be hidden was discovered bifurcation scenario its birth described. nontriviality cogency procedure localization, question detecting type remained open. This article aims give an exhaustive answer question, demonstrating both detailed formulation radiophysical localization circuit, as well thorough description relationship between modeling, computer simulation.