Hidden Attractors on One Path: Glukhovsky-Dolzhansky, Lorenz, and Rabinovich Systems

In 1963, meteorologist Edward Lorenz suggested an approximate mathematical model (the Lorenz system) for the Rayleigh-Bénard convection and discovered numerically a chaotic attractor in this model [1]. This discovery stimulated rapid development of the chaos theory, numerical methods for attractor investigation, and till now has received a great deal of attention from different fields [2–7]. The Lorenz system gave rise to various generalizations, e.g. Lorenz-like systems, some of which are also simplified mathematical models of physical phenomena. In this paper, we consider the following Lorenz-like system  ẋ = −σ(x− y)− ayz ẏ = rx− y − xz ż = −bz + xy, (1)