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Oscillation analysis of advertising capital model: Analytical and numerical studies

Author

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  • Wang, Qi
  • Wen, Jiechang
  • Zhang, Ping

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.

Suggested Citation

  • Wang, Qi & Wen, Jiechang & Zhang, Ping, 2019. "Oscillation analysis of advertising capital model: Analytical and numerical studies," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 365-376.
    • Handle: RePEc:eee:apmaco:v:354:y:2019:i:c:p:365-376
    DOI: 10.1016/j.amc.2019.02.029
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