The asymptotic behavior of solutions of the buffered bistable system.
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.
Guo
Jong-Shenq
JS
Department of Mathematics, National Taiwan Normal University, 88, Section 4, Ting Chou Road, Taipei, 116, Taiwan. jsguo@math.ntnu.edu.tw
Tsai
Je-Chiang
JC
D000818:Animals; D002021:Buffers; D002118:Calcium / Q000502:physiology*; D015220:Calcium Channels / Q000502:physiology; D005260:Female; D053496:Inositol 1,4,5-Trisphosphate Receptors; D007295:Inositol Phosphates / Q000502:physiology; D008954:Models, Biological; D009865:Oocytes / Q000502:physiology*; D018160:Receptors, Cytoplasmic and Nuclear / Q000502:physiology; D014981:Xenopus
D002021:Buffers; D015220:Calcium Channels; D053496:Inositol 1,4,5-Trisphosphate Receptors; D007295:Inositol Phosphates; D018160:Receptors, Cytoplasmic and Nuclear; D002118:Calcium