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The asymptotic behavior of solutions of the buffered bistable system

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Abstract

In this paper, we study a model for calcium buffering with bistable nonlinearity. We present some results on the stability of equilibrium states and show that there exists a threshold phenomenon in our model. In comparing with the model without buffers, we see that stationary buffers cannot destroy the asymptotic stability of the associated equilibrium states and the threshold phenomenon. Moreover, we also investigate the propagation property of solutions with initial data being a disturbance of one of the stable states which is confined to a half-line. We show that the more stable state will eventually dominate the whole dynamics and that the speed of this propagation (or invading process) is positive.

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  1. Department of Mathematics, National Taiwan Normal University, 88, Section 4, Ting Chou Road, Taipei, 116, Taiwan

    Jong-Shenq Guo

  2. Department of Computer Science, National Taiwan Ocean University, 2, Pei-Ning Road, Keelung, 202, Taiwan

    Je-Chiang Tsai

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  1. Jong-Shenq Guo
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Guo, JS., Tsai, JC. The asymptotic behavior of solutions of the buffered bistable system. J. Math. Biol. 53, 179–213 (2006). https://doi.org/10.1007/s00285-006-0381-7

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