Hierarchical structure description of spatiotemporal chaos

Spatiotemporal chaos.

Structure of characteristic Lyapunov vectors in spatiotemporal chaos.

We study Lyapunov vectors (LVs) corresponding to the largest Lyapunov exponents in systems with spatiotemporal chaos. We focus on characteristic LVs and compare the results with backward LVs obtained via successive Gram-Schmidt orthonormalizations. Systems of a very different nature such as coupled-map lattices and the (continuous-time) Lorenz '96 model exhibit the same features in quantitative...

Collapse of spatiotemporal chaos.

The transient nature of spatiotemporal chaos is examined in reaction-diffusion systems with coexisting stable states. We find the apparent asymptotic spatiotemporal chaos of the Gray-Scott system to be transient, with the average transient lifetime increasing exponentially with medium size. The collapse of spatiotemporal chaos arises when statistical spatial correlations produce a quasihomogene...

Logarithmic bred vectors in spatiotemporal chaos: structure and growth.

Bred vectors are a type of finite perturbation used in prediction studies of atmospheric models that exhibit spatially extended chaos. We study the structure, spatial correlations, and the growth rates of logarithmic bred vectors (which are constructed by using a given norm). We find that, after a suitable transformation, logarithmic bred vectors are roughly piecewise copies of the leading Lyap...

Chaos and Spatiotemporal Chaos in Convective Systems

Much of early research on chaos from the viewpoint of physics was performed using spatially confined convective systems. In spatially extended convective systems, on the other hand, spatiotemporal chaos occurs. However, there is no unified definition for the term spatiotemporal chaos as for chaos. To unify definition, a property common to the three kinds of spatiotemporal chaos observed in elec...