LYAPUNOV SPECTRAL-ANALYSIS OF A NONEQUILIBRIUM ISING-LIKE TRANSITION

By simulating a nonequilibrium coupled map lattice that undergoes an I sing-like phase transition, we show that the Lyapunov spectrum and rel ated dynamical quantities, such as the dimension correlation length xi (delta), are insensitive to the onset of long-range ferromagnetic orde r. In particular, the dimension correlation length xi(delta) remains f inite and of order 1 lattice spacing while the two-point correlation l ength diverges to infinity. As a function of lattice coupling constant g and for certain lattice maps, the Lyapunov dimension density and ot her dynamical order parameters go through a minimum. The occurrence of this minimum as a function of g depends on the number of nearest neig hbors of a lattice point but not on the lattice symmetry, on the latti ce dimensionality, or on the position of the Ising-Like transition. In one-space dimension, the spatial correlation length associated with m agnitude fluctuations and the length xi(delta) are approximately equal , with both varying linearly with the radius of the lattice coupling.