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Devil's staircase route to chaos in a non‐linear circuit
Author(s) -
Chua L. O.,
Yao Y.,
Yang Q.
Publication year - 1986
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.4490140405
Subject(s) - chaotic , bifurcation , subharmonic , mathematics , chaos (operating system) , negative resistance , order (exchange) , state (computer science) , physics , mathematical analysis , nonlinear system , computer science , quantum mechanics , algorithm , economics , artificial intelligence , computer security , finance , voltage
A driven second‐order negative‐resistance oscillator circuit has been observed experimentally to exhibit infinitely many distinct chaotic states in addition to infinitely many subharmonic responses of all orders. Each chaotic state is found to be born out of a devil's staircase whose steps are spaced in accordance with a definite period‐adding law . Each devil's staircase emerges at some level of frequency‐tuning resolution, where each level is embedded within an outer level, ad infinitum . The global bifurcation structure is self‐similar in the sense that upon rescaling, the devil's staircases appear to be clones of each other.