Abstract
In this study, a proto theoretical-model is established to explain observed experimental results. Spatio-temporal patterns, such as wave-like motion emerging in experiments, can be considered as cascading reactions of dynamic bifurcations in a two-dimensional set of closely coupled nonlinear oscillators. Each oscillator exhibits a Hopf-bifurcation between a small amplitude oscillation around the equilibrium and a large amplitude limit-cycle oscillation below the critical wind speed. Collisions among neighboring rods occur as amplitudes of rod vibrations increase with increasing wind velocity. It is possible to overcome the barrier of unstable limit-cycle in subcritical Hopf-bifurcation depending on the rate and magnitude of these collisions. Consequently, a transition from a small amplitude oscillation to a large amplitude limit-cycle, or one from a limit-cycle to a small oscillation, is generated. Thereupon, it is propagated on the two-dimensional lattice. In this manner, the two-dimensional structure of the propagated subcritical Hopf-bifurcations is proven to determine a kind of spatio-temporal pattern. Results from experiments and theoretical analyses agree well qualitatively.
