Exploring the Role of Spatial Coupling in Spatiotemporal Chaos using Covariant Lyapunov Vectors

One aspect of spatiotemporal chaos that often presents a formidable challenge is the difficulty in building a physical understanding of the role of the spatial couplings on the complex dynamics. In many systems of interest, such as fluid systems, the spatial couplings can be quite complex with both local and long-range contributions resulting from diffusive and nonlinear convective physical phenomena. We use the covariant Lyapunov vectors (CLVs) to provide new insights into the role of the spatial couplings for the chaotic dynamics of large 1D and 2D coupled map lattices (CMLs). By using CMLs we are able to explore a large parameter space and a broad variation of spatial couplings. We explore spatiotemporal chaos when there is local diffusive coupling, a weak long-range coupling, and a nonlinear convective coupling. We investigate how these spatial couplings affect the spatiotemporal features of the CLVs, we quantify the dimension and degree of hyperbolicity of the dynamics using the CLVs and lastly, we probe how the decomposition of the dynamics into physical and transient modes is affected by the spatial couplings.