Research output: Contribution to journal › Article › peer-review
Scenarios of hyperchaos occurrence in 4D Rössler system. / Stankevich, N.; Kazakov, A.; Gonchenko, S.
In: Chaos, Vol. 30, No. 12, 123129, 01.12.2020.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Scenarios of hyperchaos occurrence in 4D Rössler system
AU - Stankevich, N.
AU - Kazakov, A.
AU - Gonchenko, S.
N1 - Publisher Copyright: © 2020 Author(s).
PY - 2020/12/1
Y1 - 2020/12/1
N2 - The generalized four-dimensional Rössler system is studied. Main bifurcation scenarios leading to a hyperchaos are described phenomenologically and their implementation in the model is demonstrated. In particular, we show that the formation of hyperchaotic invariant sets is related mainly to cascades (finite or infinite) of nondegenerate bifurcations of two types: period-doubling bifurcations of saddle cycles with a one-dimensional unstable invariant manifold and Neimark-Sacker bifurcations of stable cycles. The onset of the discrete hyperchaotic Shilnikov attractors containing a saddle-focus cycle with a two-dimensional unstable invariant manifold is confirmed numerically in a Poincaré map of the model. A new phenomenon, "jump of hyperchaoticity,"when the attractor under consideration becomes hyperchaotic due to the boundary crisis of some other attractor, is discovered.
AB - The generalized four-dimensional Rössler system is studied. Main bifurcation scenarios leading to a hyperchaos are described phenomenologically and their implementation in the model is demonstrated. In particular, we show that the formation of hyperchaotic invariant sets is related mainly to cascades (finite or infinite) of nondegenerate bifurcations of two types: period-doubling bifurcations of saddle cycles with a one-dimensional unstable invariant manifold and Neimark-Sacker bifurcations of stable cycles. The onset of the discrete hyperchaotic Shilnikov attractors containing a saddle-focus cycle with a two-dimensional unstable invariant manifold is confirmed numerically in a Poincaré map of the model. A new phenomenon, "jump of hyperchaoticity,"when the attractor under consideration becomes hyperchaotic due to the boundary crisis of some other attractor, is discovered.
UR - http://www.scopus.com/inward/record.url?scp=85099234105&partnerID=8YFLogxK
U2 - 10.1063/5.0027866
DO - 10.1063/5.0027866
M3 - Article
C2 - 33380035
AN - SCOPUS:85099234105
VL - 30
JO - Chaos
JF - Chaos
SN - 1054-1500
IS - 12
M1 - 123129
ER -
ID: 86484367