Lyapunov spectrum of a lattice of chaotic systems with local and non-local couplings

We consider a one-dimensional chaotic piecewise linear map lattice with periodic boundary conditions and two types of interactions: (i) local couplings between nearest and next-to-the-nearest neighbors; and (ii) non-local couplings randomly chosen along the lattice according to a specified probability. The chaoticity of the lattice is described by means of its Lyapunov spectrum, which furnishes also information about the system global attractor in a high-dimensional phase space. We study in particular the dependence of this spectrum with the coupling parameters, as well as make comparisons with limiting cases, for which the Lyapunov spectrum is known.