Oscillation analysis of advertising capital model: Analytical and numerical studies

Qi Wang, Jiechang Wen and Ping Zhang

Applied Mathematics and Computation, 2019, vol. 354, issue C, 365-376

Abstract: This paper mainly deals with the oscillation of nonlinear delay differential equation which is used to describe advertising capital model, analytically and numerically. Firstly, the condition of oscillation of the analytic solution is presented by the technique of the theory of characteristic. Secondly, the asymptotic behavior of non-oscillatory analytic solution is verified. Thirdly, the θ-methods are applied to the mentioned equation, some conditions under which the numerical solution oscillates are obtained. Moreover, it is proved that every non-oscillatory numerical solution tends to the steady state of the model. Finally, some numerical simulations for verifying the theoretical findings are provided.

Keywords: Advertising capital model; Nonlinear delay differential equation; Oscillation; Asymptotic behavior; θ-methods (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:354:y:2019:i:c:p:365-376

DOI: 10.1016/j.amc.2019.02.029

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