Torsion-adding and asymptotic winding number for periodic window sequences

In parameter space of nonlinear dynamical systems, windows of periodic states are aligned following the routes of period-adding configuring periodic window sequences. In state space of driven nonlinear oscillators, we determine the torsion associated with the periodic states and identify regions of...

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Bibliographic Details
Published in:Physics letters. A 2013-03, Vol.377 (8), p.628-631
Main Authors: Medeiros, E.S., Medrano-T, R.O., Caldas, I.L., de Souza, S.L.T.
Format: Article
Language:English
Subjects:
Driven oscillators
Parameter space
Period-adding
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Summary:In parameter space of nonlinear dynamical systems, windows of periodic states are aligned following the routes of period-adding configuring periodic window sequences. In state space of driven nonlinear oscillators, we determine the torsion associated with the periodic states and identify regions of uniform torsion in the window sequences. Moreover, we find that the measured torsion differs by a constant between successive windows in periodic window sequences. Finally, combining the torsion-adding phenomenon, reported in this work, and the known period-adding rule, we deduce a general rule to obtain the asymptotic winding number in the accumulation limit of such periodic window sequences. ► We find that the torsion numbers of periodic states differs by a constant in sequences of periodic windows in the parameter space. ► We deduce a general rule for the winding numbers of periodic windows in a sequence. ► We obtain the asymptotic winding number of periodic windows sequences.
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2013.01.004