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Attractors and approximations for lattice dynamical systems. (English) Zbl 1173.37331
Summary: We present a sufficient condition for the existence of a global attractor for general lattice dynamical systems, then consider the existence of attractors and their approximation for second-order and first-order lattice systems which, in particular case, can be regarded as the spatial discretizations of corresponding wave equations and reaction–diffusion equations in \(Bbb R^k\).

MSC:
37L60 Lattice dynamics and infinite-dimensional dissipative dynamical systems
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