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Qualitative analysis for a biological depletion model

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  • Shi, Yao
  • Wu, Jianhua
  • Wang, Yan’e

Abstract

In this paper, we deal with a depletion model which is constructed by an activator and a substrate in a bounded domain. A better understanding of the asymptotic stability of constant solutions is obtained for such a general depletion model. The difficulty lies in how to clarify the number and the region of constant solutions. Next, we analyze the steady-state bifurcation from constant solutions. Finally, some numerical simulations are done to complement analytical results, and steady spike solutions are observed for proper parameters.

Suggested Citation

  • Shi, Yao & Wu, Jianhua & Wang, Yan’e, 2021. "Qualitative analysis for a biological depletion model," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    • Handle: RePEc:eee:apmaco:v:401:y:2021:i:c:s0096300321001508
    DOI: 10.1016/j.amc.2021.126102
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    References listed on IDEAS

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    1. Lianchao Gu & Peiliang Gong & Hongqing Wang, 2020. "Hopf Bifurcation and Turing Instability Analysis for the Gierer–Meinhardt Model of the Depletion Type," Discrete Dynamics in Nature and Society, Hindawi, vol. 2020, pages 1-10, January.
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