Research article Special Issues

Traveling waves in delayed reaction-diffusion equations in biology

  • Received: 22 July 2020 Accepted: 27 August 2020 Published: 25 September 2020
  • This paper represents a literature review on traveling waves described by delayed reactiondiffusion (RD, for short) equations. It begins with the presentation of different types of equations arising in applications. The main results on wave existence and stability are presented for the equations satisfying the monotonicity condition that provides the applicability of the maximum and comparison principles. Other methods and results are described for the case where the monotonicity condition is not satisfied. The last two sections deal with delayed RD equations in mathematical immunology and in neuroscience. Existence, stability, and dynamics of wavefronts and of periodic waves are discussed.

    Citation: Sergei Trofimchuk, Vitaly Volpert. Traveling waves in delayed reaction-diffusion equations in biology[J]. Mathematical Biosciences and Engineering, 2020, 17(6): 6487-6514. doi: 10.3934/mbe.2020339

    Related Papers:

  • This paper represents a literature review on traveling waves described by delayed reactiondiffusion (RD, for short) equations. It begins with the presentation of different types of equations arising in applications. The main results on wave existence and stability are presented for the equations satisfying the monotonicity condition that provides the applicability of the maximum and comparison principles. Other methods and results are described for the case where the monotonicity condition is not satisfied. The last two sections deal with delayed RD equations in mathematical immunology and in neuroscience. Existence, stability, and dynamics of wavefronts and of periodic waves are discussed.


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