
N.A. Magnitskii On the nature of hyperchaos in nonlinear systems of differential equations 

Abstract.
Using the example of the performed analytical and numerical analysis of cycle bifurcations of the generalized fourdimensional 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 FeigenbaumSharkovskyMagnitskii universal bifurcation scenario. In this case, due to the presence of an additional fourth dimension, the infinitely sheeted surface of the twodimensional 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. 4751.
DOI: 10.14357/20790279220205 References
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