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Existence and stability of pulse waves bifurcated from front and back waves in bistable reaction-diffusion systems

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Abstract

The existence and stability property of traveling pulse waves are shown by using the analytical singular perturbation method. The crossing behavior of stable and unstable manifolds with respect to the equilibrium points is given, which corresponds to the sign of Jacobian of the matching condition. It plays an essential part in proving the unique existence and stability property of traveling pulse waves.

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Authors and Affiliations

  1. Department of Mathematics, Toyama University, 930, Toyama, Japan

    Hideo Ikeda

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  1. Hideo Ikeda
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Correspondence to Hideo Ikeda.

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Ikeda, H. Existence and stability of pulse waves bifurcated from front and back waves in bistable reaction-diffusion systems. Japan J. Indust. Appl. Math. 15, 163 (1998). https://doi.org/10.1007/BF03167401

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  • DOI: https://doi.org/10.1007/BF03167401

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