On the problem of stability in lattice dynamical systems (Q1903054)

The authors present methods for establishing the full nonlinear stability of solutions of lattice dynamical systems. Applying the methods to a particular coupled map lattice model, the authors prove the existence of the so-called ``chaos-order'' phase transition. For that model previously it was proved that for small coupling regime there is the only equilibrium state, namely the time-space chaos. When the strength of spatial interactions increases, some new equilibrium states, corresponding to coherent structures, turn out to appear.