Linear analysis of coupled lattices

Linear analysis of coupled lattices

The parametrization of linear one-dimensional optical systems using the so-called Twiss parameters, b, a, and f, has been well established for some time [1]. The extension to two dimensions involves identifying the normal modes by transforming the full turn 4 3 4 transfer matrix to block diagonal form [2]. The system is then parametrized using the six Twiss parameters for both normal modes and ...

Failure of linear control in noisy coupled map lattices

We study a 1D ring of diffusively coupled logistic maps in the vicinity of an unstable, spatially homogeneous fixed point. The failure of linear controllers due to additive noise is discussed with the aim of clarifying the failure mechanism. A criterion is suggested for estimating the noise level that can be tolerated by the given controller. The criterion implies the loss of control for surpri...

Beam envelope calculations in general linear coupled lattices

Analytical Approach for Piecewise Linear Coupled Map Lattices

A simple construction is presented, which generalises piecewise linear one–dimensional Markov maps to an arbitrary number of dimensions. The corresponding coupled map lattice, known as a simplicial mapping in the mathematical literature, allows for an analytical investigation. Especially the spin Hamiltonian, which is generated by the symbolic dynamics is accessible. As an example a formal rela...

Extremal Coupled Map Lattices

We propose a model for co-evolving ecosystems that takes into account two levels of description of an organism, for instance genotype and phenotype. Performance at the macroscopic level forces mutations at the microscopic level. These, in turn, affect the dynamics of the macroscopic variables. In some regions of parameter space, the system self-organises into a state with localised activity and...