Toward complex behavior and synchronization in networks and chaos with strong anticipation

Since the introduction of strong anticipation by D.Dubois the numerous investigations of concrete systems had been proposed. But further development of the theory of anticipatory systems follows to 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 chains of coupled elements with strong anticipation. It is proposed the mathematical formulation of problems, possible analytical formulas for solutions and examples of presumable distributed solutions including synchronization. Multivalued behavior of such solutions is discussed.