Frequency locking in extended systems: The impact of a Turing modeA. Yochelis1, C. Elphick2, A. Hagberg3 and E. Meron4, 5
1 Department of Chemical Engineering, Technion, Israel Institute of Technology 32000 Haifa, Israel
2 Centro de Fisica No Lineal y Sistemas Complejos de Santiago Casilla 17122, Santiago, Chile
3 Mathematical Modeling and Analysis, Theoretical Division Los Alamos National Laboratory - Los Alamos, NM 87545, USA
4 Department of Physics, Ben Gurion University - Beer Sheva 84105, Israel
5 Department of Solar Energy and Environmental Physics, BIDR Ben Gurion University - Sede Boker Campus 84990, Israel
received 28 June 2004; accepted in final form 8 November 2004
published online 17 December 2004
A Turing mode in an extended periodically forced oscillatory system can change the classical resonance boundaries of a single forced oscillator. Using the normal form equation for forced oscillations, we identify a Hopf-Turing bifurcation point around which we perform a weak nonlinear analysis. We show that resonant standing waves can exist outside the 2:1 resonance region of uniform oscillations, and non-resonant mixed-mode oscillations may prevail inside the resonance region.
05.45.Xt - Synchronization; coupled oscillators.
47.20.Ky - Nonlinearity (including bifurcation theory).
47.54.+r - Pattern selection; pattern formation.
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