Lyapunov spectral analysis of a nonequilibrium Ising-like transition

Abstract

By simulating a nonequilibrium coupled map lattice that undergoes an Ising-like phase transition, we show that the Lyapunov spectrum and related dynamical quantities such as the dimension correlation length~${\xi }_{\delta }$ are insensitive to the onset of long-range ferromagnetic order. As a function of lattice coupling constant~$g$ and for certain lattice maps, the Lyapunov dimension density and other dynamical order parameters go through a minimum. The occurrence of this minimum as a function of~$g$ depends on the number of nearest neighbors of a lattice point but not on the lattice symmetry, on the lattice dimensionality or on the position of the Ising-like transition. In one-space dimension, the spatial correlation length associated with magnitude fluctuations and the length~${\xi }_{\delta }$ are approximately equal, with both varying linearly with the radius of the lattice coupling.

29 pages of text plus 15 figures, uses REVTeX macros. Submitted to Phys. Rev. E.

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• Complex Patterns in a Simple System
• Spiral Defect Chaos in Large Aspect Ratio Rayleigh-Benard Convection
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