Abstract
This chapter focuses on dynamical behavior of lattice models arising in the biological sciences, in particular, attractors for such systems. Three types of lattice dynamical systems are investigated; they are lattice reaction-diffusion systems, Hopfield neural lattice systems, and neural field lattice systems. For each system the existence of a global, nonautonomous, or random attractor is shown. The upper semi continuity of attractors for the Hopfield neural lattice model and the upper semi continuity of numerical attractors are also discussed.
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