Instabilities and spatio-temporal chaos in hexagon patterns with rotation

Instabilities and spatio-temporal chaos of long-wave hexagon patterns in rotating Marangoni convection.

We consider surface-tension driven convection in a rotating fluid layer. For nearly insulating boundary conditions we derive a long-wave equation for the convection planform. Using a Galerkin method and direct numerical simulations we study the stability of the steady hexagonal patterns with respect to general side band instabilities. In the presence of rotation, steady and oscillatory instabil...

Controlling Optical Chaos , Spatio - Temporal Dynamics , and Patterns

We describe how small perturbations applied to optical systems can be used to suppress or control optical chaos, spatio-temporal dynamics, and patterns. This research highlights the fact that complex behavior, such as chaos, has a beautiful and orderly underlying structure. We demonstrate that this orderly structure can be exploited for a variety of applications, such as stabilizing laser behav...

Collective patterns arising out of spatio-temporal chaos.

We present a simple mathematical model in which a time averaged pattern emerges out of spatio-temporal chaos as a result of the collective action of chaotic fluctuations. Our evolution equation possesses spatial translational symmetry under periodic boundary conditions. Thus the spatial inhomogeneity of the statistical state arises through spontaneous symmetry breaking. The transition from a st...

Turing instabilities and spatio-temporal chaos in ratio-dependent Holling-Tanner model.

In this paper we consider a modified spatiotemporal ecological system originating from the temporal Holling-Tanner model, by incorporating diffusion terms. The original ODE system is studied for the stability of coexisting homogeneous steady-states. The modified PDE system is investigated in detail with both numerical and analytical approaches. Both the Turing and non-Turing patterns are examin...

Spatio-temporal Chaos. Errors and Correction