Antimonotonicity: Inevitable Reversals of Period-Doubling Cascades

SILVINA PONCE DAWSON; CELSO GREBOGI; JAMES A. YORKE; ITTAI KAN; HUSEYIN KOCAK

PHYSICS LETTERS A

Año: 1992 vol. 162 p. 249 - 254

0375-9601

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.