Abstract
Strange nonchaotic attractors are attractors that are geometrically strange, but have nonpositive Lyapunov exponents. These attractors occur in regimes of nonzero Lebesgue measure in the parameter space of quasiperiodically driven dissipative dynamical systems. We investigate a route to strange nonchaotic attractors in systems with a symmetric invariant subspace. Assuming there is a quasiperiodic torus in the invariant subspace, we show that the loss of the transverse stability of the torus can lead to the birth of a strange nonchaotic attractor. A physical phenomenon accompanying this route to strange nonchaotic attractors is an extreme type of intermittency. We expect this route to be physically observable, and we present theoretical arguments and numerical examples with both quasiperiodically driven maps and quasiperiodically driven flows. The transition to chaos from the strange nonchaotic behavior is also studied.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1623-1630 |
| Number of pages | 8 |
| Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |
| Volume | 56 |
| Issue number | 2 |
| State | Published - Aug 1997 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Mathematical Physics
- Physics and Astronomy(all)
- Condensed Matter Physics
- Statistical and Nonlinear Physics
Cite this
Bifurcation to strange nonchaotic attractors. / Yaiçinkaya, Tolga; Lai, Ying-Cheng.
In: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 56, No. 2, 08.1997, p. 1623-1630.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Bifurcation to strange nonchaotic attractors
AU - Yaiçinkaya, Tolga
AU - Lai, Ying-Cheng
PY - 1997/8
Y1 - 1997/8
N2 - Strange nonchaotic attractors are attractors that are geometrically strange, but have nonpositive Lyapunov exponents. These attractors occur in regimes of nonzero Lebesgue measure in the parameter space of quasiperiodically driven dissipative dynamical systems. We investigate a route to strange nonchaotic attractors in systems with a symmetric invariant subspace. Assuming there is a quasiperiodic torus in the invariant subspace, we show that the loss of the transverse stability of the torus can lead to the birth of a strange nonchaotic attractor. A physical phenomenon accompanying this route to strange nonchaotic attractors is an extreme type of intermittency. We expect this route to be physically observable, and we present theoretical arguments and numerical examples with both quasiperiodically driven maps and quasiperiodically driven flows. The transition to chaos from the strange nonchaotic behavior is also studied.
AB - Strange nonchaotic attractors are attractors that are geometrically strange, but have nonpositive Lyapunov exponents. These attractors occur in regimes of nonzero Lebesgue measure in the parameter space of quasiperiodically driven dissipative dynamical systems. We investigate a route to strange nonchaotic attractors in systems with a symmetric invariant subspace. Assuming there is a quasiperiodic torus in the invariant subspace, we show that the loss of the transverse stability of the torus can lead to the birth of a strange nonchaotic attractor. A physical phenomenon accompanying this route to strange nonchaotic attractors is an extreme type of intermittency. We expect this route to be physically observable, and we present theoretical arguments and numerical examples with both quasiperiodically driven maps and quasiperiodically driven flows. The transition to chaos from the strange nonchaotic behavior is also studied.
UR - http://www.scopus.com/inward/record.url?scp=0000840938&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0000840938&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:0000840938
VL - 56
SP - 1623
EP - 1630
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
SN - 1539-3755
IS - 2
ER -