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

Junhai Ma; Hui Jiang; Junhai Ma; Hui Jiang

doi:10.3934/era.2022061

Electronic Research Archive

2022, Volume 30, Issue 4: 1142-1157. doi: 10.3934/era.2022061

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

Junhai Ma ,
Hui Jiang ^,

College of Management and Economics, Tianjin University, Tianjin 300072, China

Received: 07 October 2021 Revised: 19 November 2021 Accepted: 28 November 2021 Published: 14 March 2022

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.
- advertising model,
- sales promotion strategy,
- flip bifurcation,
- periodic solution
Citation: Junhai Ma, Hui Jiang. Dynamics of a nonlinear differential advertising model with single parameter sales promotion strategy[J]. Electronic Research Archive, 2022, 30(4): 1142-1157. doi: 10.3934/era.2022061

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Abstract

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.

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