Abstract. 

Using the example of the performed analytical and numerical analysis of cycle bifurcations of the generalized four-dimensional system of Lorentz equations, it is shown that the transition to hyperchaos in nonlinear systems of differential equations occurs, as in any other nonlinear chaotic systems, in accordance with the Feigenbaum-Sharkovsky-Magnitskii universal bifurcation scenario. In this case, due to the presence of an additional fourth dimension, the infinitely sheeted surface of the two-dimensional heteroclinic separatrix manifold (separatrix zigzag) is split, which contains both all singular attractors and all cycles of the system, born as a result of all infinite cascades of bifurcations.

Keywords: 

dissipative systems, bifurcations, dynamic chaos, hyperchaos, FSM theory.

PP. 47-51.

DOI: 10.14357/20790279220205