High-dimensional interior crisis in the Kuramoto-Sivashinsky equation

An investigation of interior crisis of high dimensions in an extended spatiotemporal system exemplified by the Kuramoto-Sivashinsky equation is reported. It is shown that unstable periodic orbits and their associated invariant manifolds in the Poincaré hyperplane can effectively characterize the global bifurcation dynamics of high-dimensional systems.A. C.-L. Chian, E. L. Rempel, E. E. Macau, R. R. Rosa, and F. Christianse

Spatiotemporal chaos control in two-wave driven systems

Spatiotemporal chaos control is considered by taking a one-dimensional driven/damped nonlinear drift-wave equation as a model. We apply an additional sinusoidal wave to suppress spatiotemporal chaos, and the system becomes a two-sinusoidal-wave driven system (the original driving wave with frequency ω and an additional controlling wave with frequency Ω). Numerical simulations show that when the frequency of the controlling wave is in the proper range, spatiotemporal chaos can be modified into a regular state where the amplitudes of all modes vary periodically with frequency Ω-ω while the phases of all modes evolve quasi-periodically with a running frequency Ω overlapped by a small modulation of frequency Ω-ω. The physical reason for this peculiar phenomenon is attributed to a frequency entrainment in the competition of the two external waves. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 200705.45.Gg Control of chaos, applications of chaos, 47.27.Rc Turbulence control, 52.35.Kt Drift waves,

Hysteresis in the nonlinear driven drift and KdV equations

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Hysteresis and onset of chaos in periodically driven nonlinear drift waves

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Three-drift-wave interaction at finite parallel wavelength: Bifurcations and transition to turbulence

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Spatio-temporal bifurcations in the driven nonlinear drift wave equation

SIGLECopy held by FIZ Karlsruhe; available from UB/TIB Hannover / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman