On the nature of hidden attractors in nonlinear autonomous systems of differential equations

Using the example of the performed analytical and numerical analysis of cycle bifurcations of a system of equations containing a “hidden” attractor, it is shown that the transition to chaos in the system occurs, as in any other nonlinear chaotic systems of differential equations, in accordance with the universal Feigenbaum- Sharkovsky-Magnitskii bifurcation scenario. At the same time, due to the absence of singular points and, consequently, the absence of homoclinic and heteroclinic separatrix contours, several incomplete FShM cascades of bifurcations are realized in the system, forming an infinitely sheeted surface of a two-dimensional heteroclinic separatrix manifold (separatrix zigzag) containing both all singular attractors of the system and all its unstable limit cycles.