Some Distributed Systems with Anticipation

Since the introduction of strong ant1c1pation by D.M.Dubois the numerous investigations of concrete systems had been proposed. As concentrated (discrete, ordinary differential equations) as distributed ( electromagnetic theory equations, cellular automata) systems with anticipation had been considered earlier. But further development of the theory of anticipatory systems depends on the investigations of new examples of distributed in space systems with anticipation. So in proposed paper the new examples of distributed physical models with anticipation had been considered - namely the system of hyperbolic differential equations with special boundary conditions. It is proposed the mathematical formulation of problems, possible analytical formulas for solutions and interpretations of presumable distributed solutions. Complex behavior of such solutions is discussed. A list of further research problems is proposed.