JMAT_V1_N1_RP3 A.M.A. El-Sayed M.E. Nasr Journal on Mathematics 2277-5137 1 1 29 33 Logistic Functional Equation, Existence, Uniqueness, Equilibrium Points, Local Stability, Bifurcation Analysis In this work the authors are concerned with the discontinuous dynamical system representing the problem of the logistic retarded functional equation x (t) = rx (t - r) [1-(t-2r)], t Î (0,T] and r, r > 0, x (t) = x , t £ 0. The existence of a unique solution 0 x Î L1[0,T] which is continuously dependence on the initial data will be proved. The local stability at the equilibrium points will be studied. The bifurcation analysis and chaos will be discussed. January - March 2012 Copyright © 2012 i-manager publications. All rights reserved. i-manager Publications http://www.imanagerpublications.com/Article.aspx?ArticleId=1667