Dynamics of a nonlinear differential advertising model with single parameter sales promotion strategy

Advertising and sales promotion are two important specific marketing communications tools. In this paper, nonlinear differential equation and single parameter sales promotion strategy are introduced into an advertising model and investigated quantitatively. The existence and stability of period- $nT$ (n = 1, 2, 4, 8) solutions are investigated. Interestingly, both period doubling bifurcation and inverse flip bifurcation occur at different parameter values in the same advertising model. The results show that the system enters into chaos from stable state through flip bifurcation and enters into stable state from chaos through inverse flip bifurcation. An effective control strategy, which suppresses flip bifurcation and promotes inverse flip bifurcation, is proposed to eliminate chaos. These results have some significant theoretical and practical value in related markets.