The paper presents a time delayed feedback model describing the relations between advertising and goodwill. Three different types of effects of advertising upon the dynamics of goodwill are modelled. The advertising policy of the management is incorporated into the model via a nonlinear advertising function. The advertising function controls advertising outlay e.g. by budget constraint and by the actual and the target values of goodwill. The behavior of the model is analyzed both anhalytically and numerically.
Special attention is given for deriving stability conditions for the limiting solutions.
The cases of repelling or chaotic limiting solutions are analyzed by bifurcation and state space diagrams. Several numerical examples are given.