Investigation of Complex Multivalued Solutions in Discrete Dynamical Systems With Anticipation

Since the introduction of strong anticipation by D. Dubois the numerous investigations of concrete systems had been proposed. Discrete dynamical systems with anticipation constitute one of such system class. But not very many investigations of such objects exist recently. More intensive investigationso f counterpartst o properties of common systems need- namely to stability of solutions, bifurcation diagrams, chaotic behavior. So the investigation of one modification of well known logistic equation by anticipatory property is considered. One of the most interesting properties in such systems is presumable multivaluednes of the solutions. The next issues are described : the examples of periodic and complex solutions, attractor’s properties, and dependence on the parameters.