Suppression of period doubling in symmetric systems

Details Suppression of period doubling in symmetric systems Suppression of period doubling in symmetric systems

Feb 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984phrvl..52..705s&link_type=abstract

Physical Review Letters (ISSN 0031-9007), vol. 52, Feb. 27, 1984, p. 705-708. Research supported by the California University.

Mathematics

102

Branching (Mathematics), Dynamic Stability, Nonlinear Systems, Oscillators, Period Doubling, Periodic Functions, Convection, Diffusion Theory, Mapping, Orbits, Symmetry

Scientific paper

Periodic-doubling instabilities in nonlinear dynamical systems with symmetrical periodic orbits are investigated analytically using mapping-bifurcation theory. It is shown that a symmetric periodic orbit undergoes bifurcation to a period-double orbit only under very limited conditions, and that these conditions can be ruled out for a large class of systems which includes the sinusoidally driven damped pendulum and the Lorentz equations. Applications to model equations of doubly-diffusive convection and to numerical investigations of convection with symmetry-breaking bifurcation are suggested.

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