TY - JOUR
T1 - Antimonotonicity
T2 - inevitable reversals of period-doubling cascades
AU - Dawson, Silvina P.
AU - Grebogi, Celso
AU - Yorke, James A.
AU - Kan, Ittai
AU - Koçak, Hüseyin
N1 - Funding Information:
This research was supported by the U.S. Department of Energy (Scientific Computing Staff Office of Energy Research), CONICET (Argentina), and the National Science Foundation. The bifurcation diagrams were computed using the computer program Dynamics by J.A. Yorke.
PY - 1992/2/10
Y1 - 1992/2/10
N2 - In many common nonlinear dynamical systems depending on a parameter, it is shown that periodic orbit creating cascades must be accompanied by periodic orbit annihilating cascades as the parameter is varied. Moreover, reversals from a periodic orbit creating cascade to a periodic orbit annihilating one must occur infinitely often in the vicinity of certain common parameter values. It is also demonstrated that these inevitable reversals are indeed observable in specific chaotic systems.
AB - In many common nonlinear dynamical systems depending on a parameter, it is shown that periodic orbit creating cascades must be accompanied by periodic orbit annihilating cascades as the parameter is varied. Moreover, reversals from a periodic orbit creating cascade to a periodic orbit annihilating one must occur infinitely often in the vicinity of certain common parameter values. It is also demonstrated that these inevitable reversals are indeed observable in specific chaotic systems.
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U2 - 10.1016/0375-9601(92)90442-O
DO - 10.1016/0375-9601(92)90442-O
M3 - Article
AN - SCOPUS:0001524879
VL - 162
SP - 249
EP - 254
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
SN - 0375-9601
IS - 3
ER -