Baigent, S.; Stark, J.; Warner, A.; (2001) Convergent dynamics of two cells coupled by a nonlinear gap junction. Nonlinear Analysis , 47 (1) pp. 257-268. 10.1016/S0362-546X(01)00174-2.
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A mathematical model for two xenopus cells linked by a gap junction is analysed. The model takes the form of a 4 dimensional singular perturbation problem. Depending upon the coupling strength of the gap junction and the electrogenic pumping, there is either one stable steady state or two stable and one unstable states. Convergence of the dynamics to a steady state is proved by projecting the system onto a 2 dimensional inertial manifold and applying Dulac's test together with the Poincaré-Bendixson theorem.
|Title:||Convergent dynamics of two cells coupled by a nonlinear gap junction|
|Keywords:||Convergent dynamics, inertial manifold, gap junctions|
|UCL classification:||UCL > School of BEAMS > Faculty of Maths and Physical Sciences > CoMPLEX - Maths and Physics in the Life Sciences and Experimental Biology|
UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Mathematics
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