TY - JOUR
T1 - Spatiotemporal bifurcation phenomena with temporal period doubling
T2 - Patterns in vibrated sand
AU - Venkataramani, Shankar C.
AU - Ott, Edward
PY - 1998
Y1 - 1998
N2 - This paper examines the consequences of the interaction between temporal period doubling and spatial pattern formation. We propose a simple discrete time, spatially continuous system, where the discrete time dynamics incorporates period doubling and the spatial operator imposes patterning at a preferred length scale. We find that this model displays a variety of bifurcations between different spatiotemporal states, and these bifurcations are generic in that they do not depend on the details of the model. The results from our simple model bear remarkable similarities with recent experiments on a vertically vibrated granular layer.
AB - This paper examines the consequences of the interaction between temporal period doubling and spatial pattern formation. We propose a simple discrete time, spatially continuous system, where the discrete time dynamics incorporates period doubling and the spatial operator imposes patterning at a preferred length scale. We find that this model displays a variety of bifurcations between different spatiotemporal states, and these bifurcations are generic in that they do not depend on the details of the model. The results from our simple model bear remarkable similarities with recent experiments on a vertically vibrated granular layer.
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U2 - 10.1103/PhysRevLett.80.3495
DO - 10.1103/PhysRevLett.80.3495
M3 - Article
AN - SCOPUS:0001709938
VL - 80
SP - 3495
EP - 3498
JO - Physical Review Letters
JF - Physical Review Letters
SN - 0031-9007
IS - 16
ER -